The 23-year-old continued his outstanding goal-record at Liverpool with the winner in a 1-0 victory over Stoke City in the club’s Premier League opener last Saturday.
The England international has now scored 11 goals in 15 top-flight appearances for the Reds following his £12m move to Merseyside from Chelsea in the January transfer window.
“No, not at all to be honest because I don’t have any expectations of myself,” he said. “I just try to do my best for the team every time and if I can score great, if I get an assist great, but if we win the game it’s good to be a part of it.
“It’s not about me scoring goals and being the ‘star’ of the team, it’s just about winning games and trying to get as high up the table as we can.”
Sturridge admitted he is still not feeling 100 per cent after the forward picked up a heel injury in England’s 1-1 draw with the Republic of Ireland in an end of season friendly at Wembley in May.
“I’m not at 100 per cent, to be honest,” added Sturridge.
“I don’t really know where I’m at percentage wise, but I wouldn’t say I’m as sharp as I will be, but it’s good to be out there and it’s important that I play games and work hard to get fit and make sure I’m doing as much as I can in order to get into tip-top condition.
“The injury was difficult because after I did it, I was on holiday on crutches and in a boot. That’s the time when you want to enjoy yourself.
“It was a difficult period for myself, but I thank God for helping me get through that. To be fit for the start of the season was a blessing.”
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news