Connor Goldson opened the scoring after just six minutes, before a Fashion Jr goal and a James Tavernier penalty had the Light Blues in control in the Scottish Premiership tie.
Speaking to RangersTV at full-time, Beale said: “I am happy with the three points, it keeps that run going in the league which is important. It was nice to get the win after a difficult week and I thought in the first-half in particular we were very good - the game petered out a bit in the second-half.
“Harry [Watling] works hard with the boys on set-plays and I thought it was a well-worked first goal. We obviously had a couple of shots in from Todd [Cantwell] and Antonio [Colak] and then Connor was there poaching and scoring which was a nice way to start the game.
“I thought we started well, we played with good energy, and we deserved our 3-0 lead at half-time. You saw one or two of the players were lacking a little bit in their legs in the second-half but we put a lot of energy into the first-half and a lot has gone into the week so we will get ready now for a tough game away to Hibs on Wednesday, that is my focus right now.”
The manager was pleased with the togetherness of the squad following last Sunday’s defeat at Hampden as they look ahead to a busy week of league and Scottish Cup action.
He added: “They go out and play and it is important they have got to pick themselves up after a difficult week. We try as a staff, but the most important thing is to go and play the next game and I thought first-half we were very very good.
“You could see that Kilmarnock came to try and frustrate us but the early goal from the set-play helped and then I thought we had some good play. At times our last pass let us down but I was pleased with the first-half.”
John Souttar was introduced late in the game as he made his first appearance since the opening day of the season at Livingston, and Beale says it is important his return to play is managed moving forward.
He continued: “John is a really really good player, he has had a real tough time with injury. Since I came into the building he has been a real top teammate to his fellow players when he has not been playing and it is nice to see him get out there today.
“He has only been back training with the group for a couple of weeks so it is the start of him picking up on his fitness but it is lovely to have him back. Similarly to Ianis [Hagi], these boys have been lost to the team for the whole season, it is important we don't rush them now because we want them back for the long term.”