The Light Blues blew Hearts away inside a 20-minute spell to open the second half at Hampden as a brace from James Tavernier and a terrific Scott Wright strike set up a showdown with Aberdeen next month for the first piece of silverware on offer.
And Butland believes the emphatic nature of the victory, following last weekend’s triumph over the same opponents and a 5-0 success in midweek over Dundee, underlines the team spirit within the dressing room.
Speaking to RangersTV after the victory, Butland commented: “What we’re becoming is a really solid team, everyone is pulling in the right direction, and we’re all putting in performances.
“The lads that are coming off the bench, as well as the lads waiting in the wings, are pushing everyone. We’ve got a really good group forming and performances are getting better and better. We’re really pleased at how things are going.
“There are no easy games, whether it’s in the league or the cup. You can’t expect to just blow teams away; you need to work for it which we’ve had to do.
“Even Dundee in midweek, 1-0 at half-time, we weren’t satisfied with it and we had to kick on. It was a really professional performance, solid, and I thought Tav was unreal.
“He’s been huge for us, and the boys were excellent to a man.”
Lawrence Shankland’s late consolation spot-kick deprived Butland of a fourth clean sheet in his last five games on an otherwise quiet afternoon for the goalkeeper, although he was serenaded by his song from the stands throughout the 90 minutes.
And the 30-year-old says all eyes must now be fixed on Thursday evening’s crunch Europa League clash against Sparta Prague at Ibrox.
He continued: “It was a very enjoyable afternoon; a really solid performance. We controlled the game in the first half, albeit they were a threat from free-kicks and long throw-ins, but we had some chances and we just needed a little bit more.
“We definitely brought that in the second half. They had a little go at the end, but it was quite a comfortable afternoon and a solid performance.
“It’s pretty special [to hear my song]. I’ve had some songs in the past, but none have resonated or been sung by so many people. It’s really nice to hear and long may it continue.
“That’s the beauty of playing for Rangers, that there is a game every three or four days. We’ll recover tomorrow and look ahead to Thursday where we’ll try to get an important win at this stage of the Europa League.”