Arsenal, whose last silverware was in 2005, triumphed 3-1 at Elland Road thanks to goals from Samir Nasri, Bacary Sagna and substitute Robin van Persie to set up a fourth-round match at home to Huddersfield, while Bradley Johnson reduced a two-goal deficit just before half-time with a stunning 30-yard strike.
Grayson said: "We showed some good qualities and if you're going to get knocked out of the FA Cup you might as well have it done by one of the best teams in Europe if not the world.
"They showed what they were all about. The way they started the game was quite worrying for us.
"But we got the goal which galvanised us - Bradley shoots like that in training and most of them end up in Wetherby, but he hit that one so sweetly it was a goal worthy of winning a match."
Grayson added: "This has whetted the appetite for players to face these sorts of teams on a weekly basis and I believe we have come out of the two games with a lot of credit."