Odelusi, who has come through the youth ranks at the Reebok Stadium, was on target either side of half-time to kill off Shrewsbury's hopes of an upset.
Robert Hall had given Wanderers the lead only for Aaron Wildig to bring the League One side back on level terms.
"When we first came to the football club, Sanmi was a player that we felt had a lot more to offer," said Freedman.
"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.
"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."
Freedman made seven changes to the side that drew 1-1 at Burnley on the opening day of the Championship season and was pleased with the contribution of the players that came in.
"It was really a pleasing night for me because I can start to see what my team's all about," he added. "I'm happy with the way we approached it. That's the main thing.
"It's very difficult for players when they don't get picked for the opening game of the season to then pick themselves up a few days later to play in a cup game which is a potential game we can lose.
"But their attitude and approach was fantastic which just tells you we've got a very close camp.
"It's taken me nine months to get that. It hasn't been born overnight so it's a work in progress towards that."
Shrewsbury manager Graham Turner was keen to take positives from his side's display but was frustrated with the goals they conceded.
"It was disappointing the way we conceded the goals but I think it's encouraging the way we stuck at it and the way we played at times," he said.
"We might have scored more, we got ourselves in good positions, but missed the target from several good shooting opportunities.
"We stuck to the game plan and tried to work the ball into good areas, which we have done, and we've been caught on the counter-attack by a very good side that's been quick, decisive and clinical in their finishing."