Graham scored the opening goal of the match after just nine minutes but did not celebrate due to his former connections with Swansea, whom he played for between 2011 and 2013.
However, the 28-year-old revealed after the match that he was delighted at having ended his dry spell in front of goal and was also pleased with coming away from the Liberty Stadium with a point.
"Certainly it's been a long-time coming, we had to work hard, we knew it would be tough. We hit them on counter attack and that seemed to work. We are happy with a point," BBC Sport quotes Graham as saying.
"I wanted to go crazy [when I scored] but I had a good relationship with the Swansea fans and had good times down here so that was always the case. I wasn't going to celebrate if I scored."
The result lifts Hull up to 12th in the Premier League table, while Swansea also move up a spot to 10th.