PSG booked their place in the final after edging Bayern Munich 6-5 on aggregate in a dramatic semi-final tie. The second leg at the Allianz Arena finished 1-1, with Kane scoring a stoppage-time equaliser, though it ultimately could not prevent Bayern's elimination.
The German side also felt aggrieved by key refereeing decisions, including a first-half penalty appeal for a Joao Neves handball that referee Joao Pinheiro chose not to award.
"It's tough to take right now. Over the two legs we had enough moments to have a different outcome but it didn't go our way," said Kane.
"Some decisions today didn't go our way and [we] played a lot of good football, but the final ball wasn't there.
"I think it has been a very strong season, but always in the Champions League it will come down to the final margins. We had the dream of winning all the trophies, we are good enough to be able to do that and that is why it hurts."
Luis Enrique's PSG now move on to face Arsenal in the final, which will be staged in Budapest, Hungary, on 30 May. The French champions are chasing history, aiming to become only the second club in the Champions League era, after Real Madrid, to retain the trophy.
Kane, who missed the opportunity to face his former north London rivals in the final, admitted he may not even watch the match, saying his plans remain undecided. Despite Arsenal's ambitions, he still views PSG as the strongest contenders.
"It is really even," he added. "Two totally different teams in the way they play but two very strong teams. It will be an interesting final.
"PSG being champions probably hold the right to be slight favourites but overall, two top teams going at it and it will be an even match.
"Us and PSG have a similar way of going about it. Some of the other top teams have a different style.
"That is the beauty of football, it can be anything that gets you over the line."
