The Socceroo glove-man let Alexis Sanchez’s shot slip through his hands and between his legs in extra-time, with the Gunners going on to win 2-1.
The 30-year-old was distraught at full-time, seen in tears on the Wembley pitch as his team-mates tried to console him.
"Just like to say thank you for all your messages and how sorry I am for my mistake. We gave our all and deserved to at least take it to pens," Federici said on Twitter.
"It's part of being a goalkeeper and I'm sure it will make me stronger! Thank you again for your amazing support."
Just like to say thank you for all your messages and how sorry I am for my mistake , we gave our all and deserved to at least take it pens..
— adam federici (@federici32) April 20, 2015
... It's part of being a goal keeper and I'm sure it will make me stronger ! Thank you again for your amazing support #readingfc 💙💙
— adam federici (@federici32) April 20, 2015
Federici has received overwhelming support from manager Steve Clarke as well as the club’s fans, who are organising a #flagsforfeds tribute at this week’s Championship clash with Birmingham at the Madejski Stadium.
The idea is for Reading fans to bring Australian flags to the match as a show of support for the long-serving shot-stopper.
Why I think #FlagsForFeds is well deserved recognition for a #readingfc legend. http://t.co/0N415ezxQ1 pic.twitter.com/F6ZlZdJ4Te
— Charles Watts (@charles_watts) April 20, 2015
Absolutely wonderful servant to this club. This man is a legend and such a nice person too. #readingfc #FlagsForFeds pic.twitter.com/iJsKHkhZwq
— The Royals (@Madstadder1871) April 21, 2015
A number of Federici’s team-mates also took to Twitter to show their support for him.
Disappointing result obviously but big shout out to @federici32 if it wasn't for this man we wouldn't be where we were today.
— Nathaniel Chalobah (@chalobah) April 18, 2015
And on another note I don't need to say it but @federici32 was incredible today. We would not have been there without him ❤️
— Jem Paul Karacan (@JemKaracan21) April 18, 2015