Paris Saint-Germain held on for a 1-1 draw at the Allianz Arena on Wednesday night to progress to the final in Budapest on a 6-5 aggregate.
Kvaratskhelia put PSG ahead midway through the first half and Harry Kane levelled in the 78th minute to set a frantic closing period, but Bayern could not find the goal that would have taken the tie to extra time. PSG will face Arsenal in Budapest on 30 May.
Kompany spoke to DAZN at full-time without deflecting blame or offering excuses, though he identified Bayern Munich's failure to convert in the final third as the decisive failing across the two legs.
"I don't have the ability to be disappointed for long. Of course, in the end we lost two very, very tight games against a very good opponent. We needed to be more decisive. Congratulations to Paris."
He made particular mention of PSG's defensive organisation in and around the penalty area, singling out their ability to deal with Bayern's most dangerous weapon.
"I thought our first half was actually good. Paris defended crosses incredibly well — they always defended the second balls very well. They were simply very active, and even though we got into dangerous situations, they still made sure that we maybe didn't get the final shot off."
Goalkeeper Manuel Neuer was similarly candid, pointing to a lack of clinical edge at the key moments.
"We didn't have that killer instinct in attack tonight. We were close to the final but couldn't get over the line. If we'd had a key moment and scored the goal, it's a different story."
Kompany reflected on a tie that Bayern had led 4-3 from the first leg in Paris after the extraordinary 5-4 defeat, before ultimately falling short across 180 minutes against the reigning European champions.
"We have played Paris five times — we have won twice, lost twice and drawn once, which was tonight. We tried everything, that also has to be said. PSG have so much quality. They've probably been the best team in Europe in the last two years."
He closed by framing the defeat as motivation rather than conclusion.
"The Champions League is over for us this season, but there will be another chance — and that's a motivation for me."
Bayern remain on course for a DFB-Pokal final against Stuttgart in Berlin on 23 May and are Bundesliga champions for the second consecutive season.