Pardew appeared to headbutt the City midfielder as the pair clashed on the touchline at the KC Stadium, and the incident overshadowed Newcastle's impressive 4-1 victory.
The Newcastle boss has accepted an FA charge of misconduct and requested a personal hearing, while his club were quick to hit him with a £100,000 fine.
Pardew admitted he was in the wrong immediately after the game and his apologies have been accepted by Bruce, who is keen to move on from the incident.
"As a club we accepted Alan's honesty in the whole situation, because he's been big and brave enough and he had to come out and say what he did," said Bruce.
"We don't want the images we saw last week and Alan would be first to understand that.
"We were all shocked with what we saw and Alan has to pay the consequences for that, which I'm sure he will do.
"Alan is going to take the fine and punishment and whatever is dished to him. I'm sure he'll take it and find a way to move on and erase it.
"Maybe he'll look at himself and say there have been too many incidents that he's been involved in.
"We all stand there in the technical area and get lost in it sometimes and maybe that's the wrong way to be."
Next up for Hull is an FA Cup quarter-final on Sunday against Sunderland, who are aiming for a second trip to Wembley this season having lost out to Manchester City in last weekend's Capital One Cup final.
Hull have already beaten Gus Poyet's side twice in the league this season, and Bruce feels the Sunderland boss would gladly swap their excellent cup form for Premier League safety.
"If you ask Gus Poyet he'd probably like it the other way round," said Bruce.
"They've had a wonderful run in the cups but Gus would probably have liked a few more wins in the Premier League."