The Dutchman had come with Erik ten Hag to United in the summer of 2022, but left in the off-season.
Van der Gaag, Steve McClaren, and Benni McCarthy were replaced by Rene Hake and Ruud van Nistelrooy.
“If it was an easy job, anyone could be there,' said Van der Gaag. 'Since the departure of Alex Ferguson, there have been peaks and troughs. The great thing about Erik is he always keeps looking ahead and going. You can't control the rest.
“You see with Ineos that they are on the same page as Ten Hag and dare to look ahead. But in that whole process, you do need results. In that respect, it was nice to beat Brentford last weekend.”
Explaining his United exit, he added: “What happened? Well, not so much. It is my ambition to become a head coach again, after first being an assistant at Ajax and then at Manchester United. It's great to be an assistant, but at some point you have your own ambitions again.”