Barca were 3-2 ahead on Tuesday night at San Siro stadium, before Inter fought back to eventually win the second-leg 4-3 in extra-time and 7-6 on aggregate.
Flick said afterwards, "I'm very disappointed that we're out - but I'm not disappointed about the performance of my team. They tried everything.
"We're out, but next year we'll start again and we'll make our fans, the club and everyone around us happy.
"They are a really good team, a strong team who defend well but also they have a really good striker.
"In the second half we were really good. I don't want to speak about the referee but every 50/50 decision was for them. We gave everything but in the end it was like that and that's what made me a bit sad.
“I don’t want to talk about it too much, it would not be fair to my team, who had a great performance. I don’t want to talk about the referee. I told him what I needed to say.”
Barca must analyse where to improve
While left disappointed with the result and the match officials, Flick signed off with a congratulations for the victors.
The German also said: “Today, Inter’s forwards were very good, they held the ball well and are very strong players, but also experienced. We have a young team and we need to improve; our task will be to get better. From every point of view, both defensively and offensively.
“We will analyse this match, but this is football and we can’t always win. We have to accept that. Now this game is over and we have to think about the next one, in a few days. It’s easier when you win, but we need to do it and have the hunger to win titles.
“I want to add something, since I also spoke about the referee: I want to wish Inter good luck, because they played a great match, and I want to wish them good luck in Munich.”