It was the hosts who opened the scoring in the 20th minute as Rob Harker headed beyond Wolves 'keeper Harry Beasley.
Wolves got themselves back in the game a minute before half time as Sherwin Seedorf found Dan Armstrong in the box who finished past Scott Maloney.
It was Bury who took the lead for the second time of the night in the 47th minute as Dougie Nyaupembe converted a Jay O'Shea cross.
The vistors had large spells of possession in the second half and their dominance showed - Donovan Wilson held off two Bury defenders before slotting past Maloney to make it 2-2.
And in the 80th minute, Hakeem Odoffin was found by a Dan Armstrong corner to head beyond the Bury 'keeper and send all three points back to Wolverhampton.
Sellars said, "I didn't think we started particularly well in the first half, I thought we were just a little bit off it.
"We didn't deserve to go a goal down but I didn't think we got into the game - then we got back into the game at 1-1.
"We've started the second half obviously poorly and we go behind again but after that, I thought the lads showed their quality and character.
"They showed great team spirit to get the win that we were looking for in a cup competition.
"I thought we had quality, I thought we had control of the game, I thought we played most of the game in their half - I didn't really think that they caused us lots of problems.
"I was pleased that the lads got the goals - there were some good goals today.
"Great goal from Dan (Armstrong) after a great run from Sherwin (Seedorf), then Dan plays Donny (Wilson) in who shows a great turn, and then Hak (Odoffin) with a towering header from a set-piece. That's a part of the game that we think's really important and he got us the winning goal.
Sellars was especially pleased with the performance of Sherwin Seedorf.
The Under 23s manager urged the left winger to have more belief in himself following a string of impressive performances.
"He's an exciting player - he's the type of player that I enjoy watching," Sellars said.
"Sometimes Sherwin needs to believe in himself a little bit more - sometimes it's me who's encouraging him to take people on where if you've got his pace and his ability, go and take people on.
"He's a real handful - they took their number 2 off after about 20 minutes because I think he'd had enough to be fair and gave up.
"He's a player who's really exciting."
