Les Parisiens bowed out of the competition on the away-goals rule, despite drawing in both legs of their quarter-final contest with the Catalan outfit.
"Honestly, we are very disappointed," the club's official website quotes Leonardo as saying. "We knew right from the start we were playing against an excellent side in Barcelona.
"I can't remember the last time I saw a side cause Barcelona as many problems as we did tonight.
"Apart from the very start of the match, we totally controlled the debate. We only lacked that second goal to get us through."
Despite their exit, the Brazilian reflected positively on the achievements of Carlo Ancelotti and his players.
"We are only at the start of our journey," he added. "Here at Paris Saint-Germain, everything is happening very quickly and we are trying to build something.
"Carlo Ancelotti is doing an incredible job, it's incredible what we have achieved."
PSG are currently top of Ligue 1 and continue their title challenge at Troyes on Saturday.