The two teams played to a 1-1 draw at the Allianz Arena on Wednesday evening after having played to a thrilling 5-4 result in the first leg in France last week.
"It's obviously tough to take, we lost narrowly. We matched PSG, these games are decided by small details," said Kompany after the match.
"The Champions League is over for us for now, but there'll be more moments, more opportunities and that’s also great motivation for me.
"The level of both teams was very, very high. PSG have so much quality, they've probably been the best team in Europe in the last two years. We tried everything, I have to say. Congratulations to PSG, but we'll try again."
Kompany and his squad will turn their attention to the last two fixtures of the Bundesliga season, already having won the league title but will also have a chance to secure more silverware in the DFB Pokal final against VfB Stuttgart.
Paris Saint-Germain have progressed to the final of the Champions League with a 6-5 aggregate scoreline against Bayern Munich following their second leg 1-1 draw.
Steven Gerrard believes Arsenal will head into this month's Champions League final as underdogs against defending champions Paris Saint-Germain.
Atletico Madrid manager Diego Simeone admitted his team "weren't clinical enough" after bowing out of the Champions League at the semi-final stage following a 2-1 defeat on aggregate against Arsenal.
Vincent Kompany has backed Mikel Arteta's view that English football operates in "a different world", as the debate over standards across Europe intensifies ahead of the Champions League final.
