A fine effort from the Liverpool striker opened the scoring at Wembley before Gary Cahill and Phil Jagielka struck in the second half.
And the 24-year-old was bullish in his claims that the Three Lions will not be heading for Brazil just to make up the numbers.
"For everybody it's a case of not going out there to make the numbers up. I'm a winner, all the players are winners, " he told ITV.
"It doesn't necessarily mean we're going to win the World Cup but we're winners. We'll do our best.
"We'll put 100 per cent in every training session, every match and we'll try to bring some success."
Goals from Gary Cahill and Phil Jagielka added to Sturridge's strike in the second half, but the forward admitted that the team weren't at their best with just over two weeks until their opening game against Italy on June 14.
"It was difficult because they defended well, they were very compact. We've worked very hard throughout the week also and we weren't as sharp as we'd have liked to have been.
"It was great to be out there to try and put a performance on for the fans and I'm happy with the result.
"It's not important about myself. It's about the team and the preparation for us. It's about putting in a shift, tactically, technically and doing everything possible to be in optimum shape for the first game."
Manager Roy Hodgson, meanwhile, hailed the victory as a "perfect end to a perfect two weeks", with his side now set to travel to Miami to take on Ecuador and Honduras.
"When you play against teams who get 10 men behind the ball you have to be patient, keep going. I never doubted we'd win the game," he told ITV.
"I knew they'd tire and in the end I think 3-0 is the minimum we can accept from the game."