Liverpool striker Andy Carroll had put the Three Lions ahead in the first half before former Aston Villa defender Olof Mellberg scored twice in 10 minutes after the interval to leave England facing defeat.
But substitute Theo Walcott levelled the game with a dipping strike from outside the area, and the winger’s mazy run and cross was then turned past Swedish goalkeeper Andreas Isakasson by Manchester United’s Danny Welbeck.
“I think you always have negative thoughts going through your mind, but you also have that belief that you can turn it around,” Gerrard told BBC Sport.
“I never thought at any stage of the game that we were going to lose, even at 2-1 down, because it wasn’t in general play taking us apart, it was just through our own mistakes at set-pieces.
“So that’s something we’ll address for the next game. We’re on four points and if we get a big win against the Ukraine, that will be seven points, and that will be a very good group stage.”
The 32-year-old admitted England were poor defending set-pieces but the captain did take heart from their improved attacking performance, and underlined Andy Carroll’s aerial ability.
“I’m delighted with the win which takes us on to four points, but there’s still some thing to address from that game. At the set-pieces we’ve lost a bit of concentration, and conceded two sloppy goals.
“But I thought we were a lot more bold and ambitious in our play, and we looked very dangerous going forward.”
“Andy [Carroll] was selected to play, and he thrives of crosses into the box, so anytime I get in the areas high up the pitch, it’s important I put in good service for Andy, and that happened against Sweden.”
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