The 28-year-old left the Liberty Stadium to join Sunderland in January, before linking up with the Tigers on loan during the summer.
Graham had not scored since leaving south Wales, until he popped up to grab the opener in Hull's 1-1 draw against the Swans on Monday night.
Graham's previous goal had been for Swansea in the Capital One Cup against Chelsea on January 9, his previous Premier League goal had been on New Year's Day against Aston Villa.
His far-post strike ended a run of 30 goalless games in all competitions, and a 1,626-minute barren spell in the Premier League.
By contrast, Graham scored 21 goals for Swansea in a season and a half, but felt he had to leave as his "face didn't fit" in Michael Laudrup's set-up, Graham having been brought to the club by Brendan Rodgers.
And, despite his travails over the last 11 months, he never pondered what might have been with Swansea, who won the Capital One Cup to secure a Europa League place just weeks after Graham left.
"I never regret anything in football," he said. "You have your ups and your downs and you take it, that's how it is. It is easy when the goals are flying in and stuff, but I made that decision and I stand by it.
"The move was down to the amount of games I was playing.
"I waited my time and then I got back in the team in January and scored four in four games. Then I didn't play against Everton away and he (Laudrup) played (winger) Nathan Dyer up front. I thought then my face didn't fit with the new manager.
"I felt in my own mind it was time to move on. I was 27 at the time and I want to play football, I don't want to sit around, even though I sat around for a few months waiting for my chance and felt I took it when it came. It was basically down to that."
But Graham could not speak highly enough of the support he has received from Bruce and his Hull team-mates during his time at the KC Stadium.
"He's been very good for me since the moment I walked into the club. He keeps reminding me how good a player I am, even though I haven't scored for a while," he said.
"That makes a difference. It shows he has faith in me which is great.
"But it is not just him, it is the other players, the coaching staff and the fans. Everyone has been great so I would like to thank them.
"I think you would start doubting yourself if you were not getting those reassurances, but everybody who has been around me, not just the players but my family and everything, have been superb. I have got the goal and I hope we can put this to bed and move on."
Sunderland have the option of recalling Graham from his loan in January should his goal mark the start of a productive spell.
But the former Watford, Middlesbrough and Carlisle man hopes to get the chance to continue with the Tigers.
"At the minute it is out of my hands," he said. "I have not spoken to anyone at Sunderland, I have not spoken to the new manager, obviously it was Paulo (Di Canio) who sent me out on loan.
"At the minute I am just concentrating on doing well for Hull. As I said the manager showed a lot of faith in me in the time I have been here and I want to repay that.
"I think it is a season-long loan, but if there is an option then we will have to see what happens."