Federici let an Alexis Sanchez effort slip through his legs in extra-time as Reading suffered a devastating loss at Wembley on Saturday.
Clarke described the Australian shot-stopper as distraught after the game as the Championship club's cup run came to an end.
"It's the life of a goalkeeper. Adam is obviously very upset, because he feels responsible for the defeat," Clarke told the club's website.
"It's much better in a game like this that if you have to lose you lose to a moment of brilliance. That's not the case today.
"As I said after the game, we win together, we lose together. Adam is a strong character.
"All the players are 100 per cent behind him, the staff are 100 per cent behind him - he'll bounce back.
"On Wednesday night when we play Birmingham, he'll be typical Adam Federici - one of our best players."
Sanchez had put Arsenal ahead in the first half before Reading equalised early in the second through Garath McCleary.
Clarke was full of praise for his team despite their loss.
"The team doesn't need me to stand here and say how proud I am. Everybody knows. The crowd, the supporters were behind everyone from the first minute," he said.
"The supporters were great. But I think the team probably shaded it. They were magnificent.
"Everything we spoke about, everything we asked them to [do] - tactically astute, tactically clever - always looking around to help each other.
"Denying Arsenal the space and always looking to be a threat when we went forward. And that was key for us in the game."
