At Emirates stadium, the Gunners were beaten 3-2 in extra-time.
However, Birchall told arsenal.com afterwards: “Super proud, I said to the boys after the game that football can be cruel. They’ve given absolutely everything.
“For such a young team, the way they dug in and the rollercoaster of the game, to still be pushing at the end to try and get something out of it really showed the personality they have, which is definitely a bedrock to go and have a career.
“It’s going to hurt, they’ll need the weekend maybe to get over it but then they’ve got to use that hurt on Monday and we’ll go again.”
On playing in front of a big Emirates crowd, Birchall also said: “Look around you! This is a spectacular place to come and play your football. It’s where a lot of these lads will go to bed at night dreaming of playing in the end.
“When the dust settles, I know that they’ll never forget this night. But we need to make sure that this night, regardless of the score, is a springboard to go and kick on and try to build a career.”