Steven Gerrard insists England can be a World Cup "match for anyone" if they live up to their potential and listen to what Fabio Capello says.
It was their first victory of the tournament but a vast improvement on the goalless draw against Algeria in Cape Town five days ago.
The win means England will meet Group D winners Germany in the last-16 on Sunday.
"There is relief there because the lads were under pressure and we are all so glad to be through to the next round," Gerrard said.
"All games are difficult but it's about us now. If we turn up and play close to our potential we're a match for anyone.
"We can do well if we play like we did against Slovenia, stick together, keep trying to improve and keep listening to the manager.
"His ideas and what he wants from the team are spot on.
"If we can deliver what he is asking we will be difficult to beat like we were against Slovenia.
"We have the quality to win football matches."
But Gerrard is aware England cannot afford a repeat of their showing against Algeria when they were booed off at the final whistle by their own fans.
He said : "We have done it before when our backs were against the wall and people were out there doubting us.
"We rolled our sleeves this time and produced the goods. We need to do that all the time.
"To get to the latter stage of the tournament, you need to find that consistency now.
"If we perform like we did against Algeria, I don't think we'll get another chance."
Gerrard again repeated his belief that Wayne Rooney will soon deliver goal-power.
Rooney looked sharper than in the previous two games and struck a post in the second half.
Gerrard said: "Wayne's had a bit of criticism over the last couple of days but he worked his socks off and showed quality.
"If people keep doubting him, it's up to them - but I'm certainly not. I know goals are around the corner now for Wayne."
