Arsenal's 1-1 draw at the Allianz Arena wasn't enough after Bayern came away from the first leg with a 2-0 win, and despite a penalty save from Lukasz Fabianski, Arsenal just couldn't get the goals they needed to go through.
Midfielder Oxlade-Chamberlain spoke after the game, and stated that Arsene Wenger's men just couldn't quite break down a stern Bayern defence, and said that at the top level of the game, you need to be able to have that extra quality in the final third, which Arsenal didn't have on the night.
"On the day 2-0 wasn't the best result in the first leg but we still had a chance to give it our all and to get a result," he said. "Bayern have weaknesses like any other team and when you score anyone can get nervous. When we did that we thought we had a chance but we just couldn't do it."
"Maybe we lacked a bit of quality with the final ball. At the top level you need that. The boys put in a great shift but we can be proud of our efforts."
England international Oxlade-Chamberlain also praised Pep Guardiola's Bayern, saying; "They're definitely up there as one of the best teams, there's still a lot of other good teams in the tournament. They've got some great players, world-class players and we wish them all the best now."
Bayern remain one of the favourites to lift the trophy yet again in May, whilst Arsenal have to reflect on being dumped out in the first knockout round of the Champions League.