Arsene Wenger's men had taken the lead against the Championship side at Wembley before Wojciech Szczesny erred for Reading's equaliser.
But Royals shot stopper Federici, who had up to then been magnificent in goal, committed a similar error in extra time as Alexis Sanchez netted Arsenal's winner.
Reading comments from Arsenal fans !!!! next time I'll gloat when a poor keeper throws one in in our next big game.— Ian Wright (@IanWright0) April 18, 2015
Wright also argued with some Gunners fans individually, while the general reception from those responding to him was one appreciating Wright being a 'true gent.'
Former Arsenal goalkeeper David Seaman also praised Federici, admitting he was 'gutted' for the Reading stopper after the FA Cup semi-final.
Next up for the north London side in the FA Cup will be either Aston Villa or Liverpool - who play out the competition's second semi-final at Wembley on Sunday afternoon.
Wright will no doubt want to see a better performance from Arsenal whoever they face. He will also no doubt encourage sympathy from the club's fans for any opponents who are unfortunate enough to make a crucial mistake...