The Bears showed their commitment to Cutler by offering him a seven-year, $126m (£73.7m) deal, while also shipping out Josh McCowan as a free agent.
"The number one thing from my standpoint is the way that he has invested in the Chicago Bears," Trestman told the Chicago Tribune.
"Jay has been emotionally and selflessly invested in ways that he wouldn't talk about. But he really cares about this organization and every day he's a very, very observant person and he's a very proactive person in terms of inserting himself in all areas of this building to help this organisation get better.
"It has been very, very impressive to watch how he has worked intelligently and selflessly to do that."
The new NFL season is due to get underway on September 4.