The £12 million forward led the Mackems to victory with the only strike in Saturday's 1-0 win over Wigan and is aiming principally to improve on last year's total of 12 league goals for Wolves.
"I kind of keep that [goal target] to myself," he told the Hartlepool Mail. "The first thing is to do better than last year and if I can keepimproving that will keep me happy.
"I just go out and play the game the best way I can and I do not like putting that kind of pressure [of a goalscoring tally] on myself.
|3/1||Steven Fletcher is 3/1 with Bet365 to score anytime for Sunderland against Manchester City
"You need goals and I have scored them early doors."The Scot went on to express his happiness with his start to life with Martin O'Neill's side but suggested that his early success is partly down to the reliable service of his team-mates.
"I am delighted the way it has started for me here," he continued. "When I came here, I knew I would get chances with the players we have and the delivery the boys are putting in has been fantastic.
“They are always giving me tap-ins or first-touch finishes.
"Normally there is just one player who can get a ball in like that, but we have several whose delivery we can rely on."Fletcher is eager to follow in the footsteps of former Sunderland striker Darren Bent, who hit 24 league goals for the Wearside club in the 2009-10 season.
"They are big boots to fill but hopefully I'm doing that with five goals in four games and hopefully I can keep that going," he added.
The striker also looked forward to the club's next game, against champions Manchester City, observing: "It is going to be a tough game. It always is when you go to Manchester City.
"It is on TV, so that is an added bonus for us. We will want to show what we can do."