Spurs lost to PSG in a penalty shootout after blowing a 2-0 lead in the final ten minutes to draw 2-2 in normal time.
Afterwards, Vicaro told Sky Italia: "Unfortunately, this is football, it's very difficult to accept because we did things well. They punished us in two situations and then on penalties, it's tough because we did what we promised to do.
"We were close, but it's not enough. It's disappointing, but I'm proud of these lads because, ultimately, starting with the idea of achieving certain things and doing them the way we did must give us strength, even if tonight was really tough."
On manager Thomas Frank, Vicario added: "Yes, we followed his instructions to the letter, and objectively, it worked: we wanted to hurt them on set pieces, and we succeeded.
"They have quality, and we knew we'd have to struggle. But you also have to have your game going well; that's football."