The Light Blues were superb on a frozen Boxing Day afternoon at Ibrox to make it seven wins on the spin from his first seven league matches in charge.
"I'm very pleased,” he told RangersTV. “It is the last game before the break and I am happy with the performance.
"I think it was very controlled and defensively very good - we didn't give any chances away until the last 10 or 15 minutes when we lost the ball a little bit too fast, but we created a lot of chances and we did well.
"I think the scoreline needed to be more when you see all the chances we created, but I am happy with the win, with the zero, and we can go into the break in the place we want, have a good rest and start over again in two weeks."
Gers had eight days in which to work leading into the match, and van Bronckhorst continued: "We work hard on things we want to see, no matter which team or system we play against.
"So today was really good and really controlled. I think the movement and the passing was good - we had to change our setup a little in the second half because they had a different system, but the players reacted well to the changes of formation, so I am really happy about that."
And with the winter break having been brought forward, there are now just over three weeks until Gers face Aberdeen at Pittodrie on 18 January.
"Now it is time to rest, and in the new year, we start again,” added the manager.
“So we have a good two weeks to prepare ourselves for the Aberdeen game, but also to get our message even more across to the players the way we want to play against a different system and different situations.
"We now have more time to become better and to improve our game."