Real managed to bundle United out of Europe thanks to victory at Old Trafford.
"It was amazing," Butragueno told manutd.com. "I think you must be very proud of your fans and the fans have to be very proud of the team really.
"We know that winning here is really difficult for any team and we realised why the other day. It really was a very intense tie and very even but, finally, we were able to get through.
"To win here was always going to be very, very difficult because United are a great team. Even when you were 2-1 down with 10 men, you played very well in the last 15 minutes and we had to face many difficulties in qualifying."