Thomas Muller acknowledged Bayern Munich needed some good fortune to overcome Paris Saint-Germain and reach the Champions League quarter-finals on Wednesday.
Julian Nagelsmann's side were indebted to Matthijs de Ligt's goal-line clearance from Vitinha in the first half at Allianz Arena after Yann Sommer's error offered the PSG midfielder an open goal.
De Ligt subsequently hooked off the line, keeping Bayern 1-0 ahead in the tie after Kingsley Coman's first-leg strike, before Nagelsmann's men seized control of the return meeting.
Eric Maxim Choupo-Moting came back to haunt his former side PSG with a second-half strike before Serge Gnabry sealed progression, though Muller was thankful for the fine margins fell for Bayern.
"You have to be honest, in a football game like this there are always moments when you need luck on your side," Muller told DAZN.
"We had that one moment when Yann loses the ball, which Matt clears the ball on the line. If it goes to 1-0 there, you don't know how the teams will react to that.
"But we shed our shyness in the second half in particular, we were clearer in defence, so we played the better game in the second half and deserved to win."
A 3-0 aggregate triumph saw Bayern progress to the Champions League quarter-finals for the 21st time, no other club has managed to reach the last eight as often.
A battling performance, coupled with clinical finishing, marked continued progression under Nagelsmann, whose side have put a poor start to 2023 behind them to fight back in the Bundesliga title race.
Nagelsmann was disappointed with what he saw in the first half as PSG twice went close to levelling the tie on aggregate, but the Bayern coach was impressed with his team's second-half response.
"In the first half we did what we discussed before the game wrong, PSG pulled a lot of players into the build-up, we then let ourselves be pulled into position, were too impatient," he told DAZN.
"The spaces were too big. We had a lot of space with the ball, but we were too scared.
"We didn't do that anymore in the second half, we won the ball well and gained a lot of depth down the right. We were clearly better in the second half and deserved to win."
Tuchel bemoans lack of focus as Bayern slump to final-day defeat
Departing Bayern Munich coach Thomas Tuchel was unhappy with his team's lack of focus following their 4-2 loss at Hoffenheim on Saturday.
Bayern threw away a two-goal lead, condemning them to a third-place finish behind unbeaten Bayern Leverkusen and Stuttgart
After failing to win the Bundesliga title for a 12th consecutive season, Tuchel's side will also go without domestic or European silverware for the first time in more than a decade.
"We started really well, but then we had a string of individual mistakes," Tuchel said in a short press conference.
The coach is leaving Bayern after just over a year in charge after the club announced his departure in February. There had been talks to potentially reverse that decision last week, but no agreement was reached.
"In the second half we played well for 15 minutes, but then it was again a series of individual mistakes and loss of possession," Tuchel said. "We gave away a two-goal lead for a completely unnecessary and bitter defeat."
Despite a string of injury absences, Bayern were 2-0 up by the sixth minute but Hoffenheim scored four times, including an Andrej Kramaric hat-trick in the second half to turn the game around.
"It happens far too often, like that. It happened in Stuttgart where we conceded two late goals [for a 3-1 defeat]. In Heidenheim, the same [for a 3-2 loss]. Here the same. It just happens too often," Tuchel added.
"I have an explanation for that, but it is not for the public."
Bayern's Aleksandar Pavlovic, who is part of Germany's preliminary Euro 2024 squad, went off injured early in the match and will undergo further tests.
"He twisted his ankle. We will have to wait and see what the checks show," Tuchel said.
Hoffenheim 4-2 Bayern Munich: Tuchel bows out on defeat thanks to Kramaric hat-trick
Bayern Munich squandered a two-goal lead to slump to a 4-2 loss at Hoffenheim courtesy of a second-half Andrej Kramaric hat-trick in Thomas Tuchel's final game.
Early goals from Mathys Tel and Alphonso Davies saw the injury-depleted Bavarians go 2-0 up by the sixth minute.
Hoffenheim, however, pulled a goal back through Germany international Maximilian Beier just two minutes later, with the hosts gradually taking some of the early pace out of the game.
Bayern's injury troubles were further compounded when they lost Aleksandar Pavlovic to injury in the 35th minute, and struggled to cope with Hoffenheim's threat in the second half.
Kramaric then delivered a stunning 19-minute hat-trick with the Bayern defence in ruins, ending a disappointing season in third place with 72 points.
Bayer Leverkusen finished in top spot on 90 points. VfB Stuttgart finished runners-up on 73 with a 4-0 demolition of Borussia Moenchengladbach, while Hoffenheim finished seventh, in the Europa Conference League place.
Data Debrief:
Thomas Muller made his 473rd Bundesliga appearance for Bayern on Saturday, drawing level with Sepp Maier as the club's record appearance maker in the competition.
Bayern failed to have a single shot on target in the second half, while Kramaric ran riot to subject Bayern to their worst league finish since 2011.
Al-Nassr 1-1 Al-Hilal: Mitrovic scores last-gasp penalty
Aleksandar Mitrovic scored a penalty in the 10th minute of second-half stoppage time as Al-Hilal denied Cristiano Ronaldo's Al-Nassr victory in a 1-1 draw.
Mitrovic netted his 27th Saudi Pro League goal of the campaign after Sadio Mane was harshly judged to have fouled Saud Abdulhamid in the area.
Mane stuck out an arm to shield the ball, catching his opponent in the throat, though the contact appeared to have been outside of the box.
Mitrovic made no mistake to keep Al-Hilal's unbeaten campaign going.
The Serbian's spot-kick cancelled out Otavio's first-minute opener, with Ronaldo having set up his compatriot.
Champions Al-Hilal remain 12 points clear of Al-Nassr at the summit of the Pro League standings.
Data Debrief: Ronaldo the provider
Ronaldo leads the scoring charts in Saudi Arabia this season, though he had to settle for an assist on Friday.
That came from the only chance he created, with the 39-year-old limited to 25 touches, though he did have four shots.
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