Tied 3-3 on aggregate after extra-time, the 32-year-old saved two penalties in the shoot-out to see Barry Ferguson’s men into the last eight.
Speaking to RangersTV at full-time, Butland said: “That is what you work for, those are the moments as a goalkeeper that you live for and not everybody gets to do it in front of a fanbase like ours. In that sense, it is as special a night as I have had in football and hopefully we continue to have those.
“It was tough, we came up against a good side, but the atmosphere tonight from start to finish was great. It is difficult to go behind in the game and to mentally stay with it because you don’t want to be losing but the boys stuck to the task.
“We had a good little reset at half-time and then we conceded again but the lads were brilliant from start to finish, in both legs.
“You can argue about possession and all that, but we deserved it, we really did. We have had some moments in penalties in the past, and we have also had tonight, which is what dreams are made of, so I really enjoyed that.”
On the character shown by the squad to keep battling in the tie and step-up in the shootout, he said: “It has been there, but that is the manager in a nutshell what we have just seen out there.
"You have seen it in the lads throughout Europe across the year but that is what we need to be about.
“It has been a brilliant couple of weeks, it has been emotional, it has been demanding but that is what it is about when you play for Rangers, and you get your rewards and we did tonight.
“Penalty shoot-outs are great for the goalkeepers when you are on the winning side and that is how it feels but I said to all the lads that the effort, the work rate and some of the football at times was top and we deserved it.”