Mikel Arteta has pushed Arsenal to leverage the "pain" of losing to Bayern Munich in the Champions League quarterfinals to strengthen their Premier League title challenge.

Bayern won 1-0 in the second leg and 3-2 overall as Joshua Kimmich's header in the second half denied Arteta's team their first semi-final appearance since 2009.

It was a bitter evening in Munich for Arteta and his team, who had hoped to guide Arsenal to their first Champions League victory.

Arsenal has had a nightmare week following a scorching run that propelled them to the top of the Premier League and into the round of eight of the Champions League.

They didn't perform well in the 2-2 first-leg draw with Bayern, and they gave up first place in the Premier League on Sunday when they lost 2-0 at home to Aston Villa due to two late goals.

After putting on yet another lackluster performance in Germany, Arteta must find a way to restore his team's damaged morale in time for a final push for the English title.

"We were very close, that is the reality. It's painful, but we have to learn from this. We had our moments, especially in the first half," Arteta said.

"The players did their best, but we didn't have that magical moment that we needed in the competition.

"In the first leg, we conceded two avoidable goals, which significantly impacted the draw.

"We were still alive when we arrived here. The margins are so fine. A mistake or a moment makes the difference."

After a lengthy absence from the Champions League, Arsenal largely acquitted themselves well.