David Ngog scored an outstanding opening goal before Tangerines forward Tom Barkhuizen's netted a controversial equaliser just before half-time.
But Ngog then worked hard to set up Jermaine Beckford for the winner on the counter-attack in the second half as Bolton progressed through at the expense of their Sky Bet Championship rivals.
Freedman, whose side are in the bottom seven of the Championship standings with only six wins from 24 games this season, said: "I like a cup run. It helped us last year where we beat Sunderland and that got our season going.
"It was a good old fashioned cup tie today and I would rather be in the next round then not."
He added of his side's performance: "David was fantastic but I don't like singling out any individuals. I felt that our desire in attack was right up there.
"We could've defended some situations a little bit better but the real honesty and desire of the players to win was the most pleasing thing."
Freedman also stated his intentions in the transfer market, but did admit he may need to sell to bring players in.
"The four guys at the back have played most of our games and we've only really got those four defenders in the building so that's where we're looking to strengthen," he said.
"But we've got to cut our cloth accordingly and look for the right sort of deals. It's a fact, that's where we are right now and it's about getting the right deals in.
"I've got to make sure that I work really hard to get things right in the transfer market but the guys upstairs have been really good to me and they've always supported me."
- Sports & Recreation
- Tom Barkhuizen