Skipper David Beckham vowed England would improve after a tense 2-0 win over World Cup debutants Trinidad and Tobago booked their spot in round two.
Beckham is positive about England's prospects
Beckham said he was always confident England would win despite having to rely on two late goals.
"We never give up. That's the message we give out - that's the message we always give out," said the midfielder.
"You've not seen the best of us yet. We know we can play better and there's better to come."
Beckham's cross set up Peter Crouch's 83rd-minute opener, with Steven Gerrard adding another goal in stoppage time.
"We knew it wasn't going to be easy today, people expected it to be easy but we knew if we kept at our game plan we would break them down," said Beckham.
"The good thing about the game is that we finished strongly."
Beckham praised coach Sven-Goran Eriksson for bringing on Wayne Rooney as a second-half substitute, alongside Aaron Lennon.
Rooney was playing in his first game since breaking his foot on 29 April.
I'm rather pleased - the players showed a lot of patience and that paid off
England coach Sven-Goran Eriksson
But the captain said: "He is ready now. He needs to get on and get fit and the manager made some good substitutions - very positive - and we pushed forward from that."
Eriksson said he was satisfied with the performance, which followed Saturday's 1-0 win over Paraguay.
"I am rather pleased, the players showed a lot of patience and that paid off," said the Swede.
He backed striker Michael Owen, who was replaced by Rooney after 58 minutes, having also failed to last an hour against Paraguay.
"I think he gets better and better. He is another player who hasn't played football for a long time," said Eriksson of Owen.
"We must now immediately begin our preparations for the game against Sweden. We haven't beaten them for a long time, so it would be nice to do it in Cologne."
Owen, meanwhile, admitted his last two outings in an England shirt "have not been my best".
"Obviously I'd like to play fantastically well in every game," he said, "but I feel I'm making good runs."
Goalscorer Crouch, who had missed decent chances earlier in the game, admitted England were "lackadaisical" at times.
But the Liverpool striker added: "Three points are all that matters, to be honest.
"We are through to the next round and we would have taken that before the game."