Adams said: "The boys are feeling flat in there. They thought they had won it.
"But I'm proud of them. This was the best performance I've seen from us in a long time. And we can still say we are four games unbeaten now, including against Milan."
Milan, who have already beaten Portugal's Braga - Pompey's 3-0 conquerors last month - and Holland's Heerenveen are through to the last 32 after the draw.
Adams said: "We've given ourselves a chance but we will still have to get over this.
"The boys are really upset they didn't hang on to win. It's my job to lift them and we can do that with another performance against Blackburn on Sunday.
"Results are what you need but at the moment I'm looking for performances - and these players are giving me them.
"I think my job is based on producing a team that will really go for it at Fratton Park and get this crowd really excited. I was amazed by our fitness levels against Milan.
"We had so many players out injured but to have Kanu back playing like that for 80 minutes in his first start since the FA Cup final was fantastic. He's finished with a bit of a groin strain."