The forward is keen for a run in the FA Cup with his new side.
The forward is set to make his second start for the Black Cats in their fourth round tie against Fulham at the Stadium of Light on Saturday, and is keen to reach the final once again.
Defoe was cup-tied when former club Portsmouth reached the final of the competition in 2008, and thus forced to watch their subsequent win against Cardiff from the stands.
He then reached the semi-finals with former club Tottenham, and now wants to make up for lost time after missing out on what would have been one of the best moments of his career.
"I was gutted, it was really hard, to be honest. I still lifted the trophy, though I was in my suit when I lifted it,” he said to ESPN.
"It was really hard. I was happy for the boys, for the team - I was a part of it, even though I didn't play because I was cup-tied. But the whole day was special and obviously you want many more of those days, so I'll look forward to this game this weekend. Hopefully we can win and progress."
The FA Cup has proved a competition in which Defoe has prospered in the past, with him currently having 22 goals in 35 appearances in the competition, and the forward is keen to add to that collection if he is handed his home debut on the weekend.
Despite Premier League survival being of high priority for the Black Cats, the forward is desperate to once again play in a competition he has not competed in since the 2011-12 season.
"I have always enjoyed playing in FA Cup games. It's a special competition, one of the best competitions in the world, and everyone is looking forward to it,” he said.
"Obviously, it's been a long time for me since I played in the FA Cup, so I am looking forward to it. It's a big game, at home. It's important that we approach it like any other game and try to win."