The Gers' hard-fought 1-0 cinch Premiership win over an under-strength Dundee United side at Ibrox on Saturday - thanks to a James Tavernier penalty - took the champions seven points clear of Old Firm rivals Celtic at the top of the table.
Former Rangers, Arsenal, Barcelona and Holland midfielder Van Bronckhorst has won seven and drawn one of the eight games as Light Blues manager since taking over from Steven Gerrard.
Romania international Hagi - who was named sponsors' man-of-the-match against United, although the bemused reaction of the home support suggested they did not concur - is glad to be continuing his football development under the Dutchman.
The 23-year-old attacker said: "I had the privilege to be coached by Steven Gerrard and I improved a lot as a player and I think I have become a more complete player.
"I learned the team part of football that I wasn't used to.
"And now being under a coach that has played at the highest level, a leader, a captain for the national team as well in his time, it is just a privilege and I just want to bring my game to the next level.
"The way he thinks about football, I love it and I see myself playing in different positions and I just enjoy it.
"I am not taking anything for granted and every second at the training ground and at the stadium I am trying to learn.
"I am being open to playing different positions and just trying to get my game to the next level, it is that simple for me."
United boss Tam Courts revealed after the game that five players out of the six missing from the team who lost to Livingston the previous week had tested positive for Covid-19.
Goalkeeper Benjamin Siegrist, Kieran Freeman, Ian Harkes, Jeando Fuchs, Ilmari Niskanen and Peter Pawlett were all absent which led to the United manager starting with four teenagers including 16-year-old Craig Moore, who made his debut before being carried off on a stretcher in the second half with a calf injury.