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."
"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."
