The 20-year-old, who came through the club's youth system, struck either side of half time to book Bolton's spot in the second round of the competition.
"When we first came to the football club, Sanmi was a player who we felt had a lot more to offer. I've got to give full credit to Jamie Fullarton who got hold of him and he's got our Development squad working really hard," Freedman told PA.
"That's what I like to do when these cup matches come along. I don't want to go and buy anyone else. I want to look at my Development squad and pick them. When I first came in, he was just in a lull but I see potential in him so we've really just worked with him.
"You've got to get on the training ground and work with them and Jamie's done that. He's popped him up to us at the beginning of the season and he's working hard. The young guy deserves everything he gets."
Odelusi had previously been linked with a loan move to a number of League One clubs.