And Campbell told ESPN: "I think we deserved it, we kept on probing, played some great football and created some great chances and it was all down to Nicklas knocking one in at the end.
"It was a tight game, but the main thing is we got the win."
Hull's goal came from a disputed Jimmy Bullard penalty after Campbell bundled over Jan Vennegoor of Hesselink, who appeared to be offside at the time.
Campbell argued: "I think he came from an offside position and the ball was behind his head so technically it was a coming together."
Bendtner missed a string of chances against Burnley last week but bounced back with a Champions League hat-trick against Porto and added the crucial strike on Saturday evening.
He told ESPN: "It felt really good, so long in coming and at 1-1 it was really tense and we were trying to push on.
"All goals you score are important, especially today and I'm pleased for the team that we won the game."
Manager Arsene Wenger added: "We started well, when we were 1-0 up we lost our focus and took it a bit too easy.
"When it was 1-1 I knew we had to battle because suddenly Hull's belief raised. We needed to fight until the last second and fortunately we got the late goal."
The Tigers played much of the game with 10 men after George Boateng received a second booking for a crude challenge on Bacary Sagna.
Wenger said: "Unfortunately he deserved it but you can understand these challenges. If teams are fighting not to go out of the Premier League you understand that commitment."
Hull boss Phil Brown was reflective after seeing his side finish empty-handed.
"It's not consolations you're after, it's positives," he said. "There have been question marks about our fight, commitment and spirit at this football club but it was there for everybody to see.
"We were down to 10 men, we had lost our most experienced player which was disappointing, but the players showed spirit. We've asked for it for nine more games and if we get it we'll be fine.
"Today was an outstanding performance from more or less every individual in the team."
Asked if Boateng had let the team down with his dismissal, Brown added: "George didn't let us down. George has never let me down since he came to the club."