Bayern Munich head coach Vincent Kompany was defiant following his side's 2-1 defeat at home to Inter in the first leg of their Champions League quarter-final on Tuesday.

The hosts trailed for much of the game after Lautaro Martinez put Inter a goal up on 38 minutes and, while Thomas Muller equalised on 85 minutes, David Frattesi restored the Nerazzurri's lead with just two minutes remaining.

“We had the chances to score more than once tonight, two or three, or even more." said Kompany, as reported by One Football.

"We know they have quality up front, it’s never unthreatening, but we were more dangerous and we had chances.

"I know Inter away from home is tough, but I don’t think we need to come out defeated because of injuries or things like that. We’ll have our chances in Milan too.

"We’ve lost, so I can only talk about what I felt or observed. I didn’t have the feeling we couldn’t score, that we couldn’t be threatening. We had our chances until the last, but results don’t always have to be fair.

"It’s half-time, but no team goes into the changing room 2-1 down at half-time and says, 'I give up; let’s go home'. The result is what it is, but we feel we can go and win in Milan,"

Veteran Muller came off the bench to score the equaliser just days after confirming that he will leave Bayern at the end of the season, having spent 25 years at the club.

The 35-year-old was in agreement with Kompany in that there was plenty left to play for in the tie.

"We know that there's definitely still a lot to play for. We had certainly imagined the first leg to turn out differently. But we know that there's definitely still a lot to play for," he said.

"We tried to come back and we did. We needed to deal with the situation before we conceded the goal to make it 2-1 better. Maybe we were a bit too cautious at the start, even though we wanted to be aggressive."

Austria right-back Konrad Laimer, meanwhile, was frustrated after Bayern let the game get away from them, having controlled it for long periods.

"We should have gotten more out of the game. We did a lot of things well over long periods of time. We knew beforehand that Inter are a good team and will have their moments," he said.

"They had their moments and capitalised on them. Now it's time to recover, play Dortmund on Saturday and then we'll turn our attention to next Wednesday, it's only half-time.

"It's important that we're full of strength and energy again. The chance of winning in Milan is definitely there.

"We have enough quality and resources to beat them. Games like this are decided by small details, as we saw today. We definitely have what it takes to win."