Celtic were left heartbroken after Bayern Munich's last-gasp winner sent them out of the Champions League but Brendan Rodgers believes his side have restored their European pride.

Alphonso Davies bundled home a stoppage-time equaliser on Tuesday, sending Bayern through as 3-2 aggregate winners after a 1-1 second-leg draw at the Allianz Arena.

Timed at 93 minutes and 12 seconds, Davies' heroics marked Bayern's latest equalising goal in a Champions League game, excluding extra time, since records began in 2003-04.

Rodgers was left to rue the late disappointment but lauded his side's efforts after Nicolas Kuhn's 63rd-minute strike gave Celtic hope in Munich.

"It was [a sucker punch], not what the players deserved especially right at the very end," Rodgers told Amazon Prime Sport.

"They gave so much to the game, they played with confidence. We didn’t give away too much, I felt our concentration was good and denied them space, and then we had quality and some great moves, and actually had the best chances in the game I felt.

"A real heroic performance, just unfortunate at the end. It was just such a cruel way to not even lose the game but to go out of the competition.

“I think our European credibility has been restored this season, I think we’d built that up from last year, that’s my takeaway from this season.

"I think we have shown real quality at times, if you think of the last time we were in Germany and the improvements we have made now."

Celtic were hammered 7-1 by Borussia Dortmund in the group stage but produced a much-improved performance on their return to Germany.

The visitors could have edged level earlier on in Tuesday's clash as well, if not for missed chances from Callum McGregor, Kuhn and Daizen Maeda.

Rodgers remained buoyant with Celtic's attempts against the Bundesliga giants, though admitted further squad improvements are needed to compete at the highest level again.

"I think we need to improve the squad again," he added. "At this level you need to be able to bring quality off the bench as well and have that freshness. That's the next step for us. 

"But I think this season has been so good. We have played some amazing football, we've had adverse moments but recovered.

"My objective is to make us a seasoned team at this level that you can consolidate. 

"Now our job is to learn from it, learn from the experiences we've had, and finish the season really well. We need to get back into the Champions League next season and let's see if we can improve again."

Celtic have now failed to win any of their 16 away games against German teams in major European competitions (D4 L12).