The manager was pleased with his squad as he was able to make eight changes ahead of a big week, with Cyriel Dessers and Danilo on the scoresheet to send Rangers into the last eight of the cup.
Looking back on this afternoon’s tie, Beale said: “We started the game quite well, we were getting the ball out to Rabbi [Matondo] and he was dominating that one v one.
“He is unfortunate not to score early in the game. It was a good save from the keeper, he also goes around the keeper and has one off the line and then I felt like we were a bit wasteful again.
“We went in at half-time and we had to have a little bit of a chat about our quality in the final third but then straight away we gave away the penalty. Cyriel [Dessers] has pulled his leg back to clear the ball and the guy has nipped in front so we can't argue about that.
“We then pushed and pushed and obviously got our penalty and our goal in front. I think Jamie MacDonald has made three or four really big saves, one from Sima and one from Hagi as well and a couple of other moments.
“We are delighted we are through, it was very similar to Partick Thistle and Raith Rovers last year but the most important thing is we are through. We have made eight changes with a view to having lots of energy and everybody fit and available for Tuesday night and my focus is already on that game now.”
The manager praised the performance of midfielder Jose Cifuentes, who picked up the Rangers’ man of the match award, as well as 20-year-old Johnly Yfeko who made his first competitive start for the first-team.
Beale continued: “We were clearly the stronger team in the game, I thought Dougie [Imrie] had his team very well organised and they were very stubborn, but it was just a matter of when we were going to score.
“I would like to say Jose Cifuentes was very good again today and I was very pleased with Johnly Yfeko so well done to him also.
“Danilo scored and Cyriel [Dessers] did fantastic in that goal tracking back, winning the ball and it was an excellent pass and which Danilo did well to finish it off.
“The numbers are coming in that sense. I would like it to have a lot more quality and rhythm at times, that is for sure, everyone can see that but with the eight changes and bearing in mind what has gone before this game and what is coming, I am just glad we are through and now we can focus on Tuesday.”
Beale has called for a big push from the squad, staff and supporters ahead of a huge evening at Ibrox on Tuesday.
Rangers host PSV in the first-leg of the UEFA Champions League play-off and the manager knows it is an important week for the squad.
He continued: “It was important that I gave people today the chance to stake their claim, it has firmed up my thoughts for Tuesday and what we'll need.
“We are going to need a big push from the crowd with them as the extra player in the stands. We will try to provide energy and really go for the game against a quality team.
“It is a two-legged cup final and in between that we have a trip up to Dingwall but let's get our focus on Tuesday, that is everybody, the fans, the players and the staff and make sure we have a right go at this game.