Ibrox chairman Sir David Murray revealed at the weekend that Rangers failed in their bid because he was unwilling to blow the club's wage structure in a bid to land the 22-year-old.
Brown added: "I hope I play every week, I want to play every week. If I don't, I'm going to have to show the gaffer what I'm made of in under-21 games and in training. I've learned under every manager. I learned under John Collins and Tony Mowbray and I will learn under Gordon Strachan as well."