James Tavernier’s second half penalty was the difference between the Light Blues and Dundee United at Ibrox, with the boss delighted to see his side get over the line.
Van Bronckhorst told RangersTV at full-time: "It was a difficult game and I think we saw a Dundee United team who did everything to give us a challenge, and they did.
"It was a really good performance by them, and I think our performance wasn't the way I wanted or the way we want the team to play, and that is why we struggled to make and create chances.
"In the second half, we created a bit more danger and we had to score and we got a couple of chances to score, and of course, from a penalty, James is very good at them and that really helped us, but United kept pushing us to try to score for 1-1, but in the end, I am really happy with the points but not happy with the performance."
The manager praised the impact of his two second-half subs, Scott Wright and Joe Aribo, for their influence in tipping the game in the balance of Gers.
Van Bronckhorst added: "We said at half-time, it was difficult to create chances, especially because they had a good organisation and a lot of players behind the ball, and it was difficult for us to create a chance.
"But when the game is progressing, you get more space, especially when Scott came in on the right to give us more speed on the flanks.
"Joe is a very important player and I had to get him in as we had to score, and he was positive again, and Wright did really well, so I am pleased with the guys we can put in a game."
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