The League One side took the scalp of Premier League outfit Rangers with a superb 4-2 win at Loftus Road.
MK Dons raced into a 2-0 half-time lead thanks to an own goal from Armand Traore and Ryan Lowe's strike with Ryan Harley and Darren Potter making it 4-0 in the second half before Jay Bothroyd and Fabio da Silva netted two late consolation goals for the hosts.
It is the first time in the club's history that MK Dons have reached the fifth round and Robinson was delighted with the achievement.
"It's a remarkable achievement," said Robinson. "We all deserve this. It will live with us for a long, long time.
"We felt we had to play in a certain way, and we felt they were going to have a lot of the ball. Granero and Faurlin were going deep and we had to prevent that. The quality they had, we knew they could crucify us, so we knew we had to be in the game at half-time, and then we could go out and enjoy it.
"But to be 2-0 at half-time...did we deserve it? No. Did we deserve to win? Yes. We deserved to be in it.
"And to come to a Premier League club and put on a show like that in the second half was tremendous. But I'll be honest, was I nervous in the last three or four minutes? Yes!
"I was desperate for the clock to go down! We've just won 4-2 at Loftus Road, so I'm not going to be too disheartened by how we defended!
"Today is a great day, but we've got Yeovil away now, and we have to prepare for them.
"I stayed at the club to get them out of this league, but days like this are special."