Bayer Leverkusen boss Xabi Alonso says his team "have to know how to suffer and fight" after their Champions League win over Milan.

Victor Boniface scored early in the second half at BayArena on Tuesday, and though Milan hit the woodwork as they searched for an equaliser, the Bundesliga champions held firm.

Leverkusen have now taken six points from their opening two Champions League matches.

After dominating the first half, in which they mustered six shots on target – only once ever having more on record (since 2003-04) when facing Real Sociedad in October 2013 (seven) – Leverkusen were less convincing following Boniface's goal.

But Alonso put that down to fatigue following Leverkusen's 1-1 draw with Bayern Munich on Saturday, in which his side were largely dominated but held on for a point.

"I think it's great news that German football is competitive. It's good news for us too to have achieved this result against Milan," Alonso told Sky Sports.

"Our first sixty minutes were good but in the end we suffered from fatigue after the game against Bayern Munich.

"We showed spirit and character, these three points are very good. In the Champions League you have to know how to suffer and fight, not just play well.

"We struggled a lot to score but maybe after the goal we changed our approach too quickly. Maybe we lacked something on a physical level.

"We had the right respect and took them very seriously. The last 20 minutes were not quite as good, but the players gave everything to get the three points."

Leverkusen are now unbeaten across their last ten home games in major European competition (W7 D3), their longest such run in club history.