Brown quit his Fir Park role on Thursday night, 24 hours after publicly reaffirming his commitment to the club in the wake of interest from the Dons.
The former Scotland manager claims he had a verbal agreement with Motherwell that either party could end the relationship without compensation.
"I was there in the 70s, fourth in the league and two semi-finals.
"I have a great affection for Motherwell and I hope it's reciprocated. I don't see why it shouldn't be.
"The commitment I gave in the 70s and last year - we answered a call, we went to Motherwell and did our best, and we've answered a call here. I don't think it should be an issue."