England manager Sven-Goran Eriksson expressed satisfaction at his team's opening World Cup victory but admitted the performance left room for improvement.
Carlos Gamarra's own goal, flick-heading a David Beckham free-kick into the Paraguay net, gave England an early lead.
But they struggled through the second half, with Paraguay threatening to snatch a point from the Group B clash.
Asked whether England might perform better in their next match, in five days' time against Trinidad and Tobago, Eriksson said: "I hope so.
"You always try to do better but I'm happy today. We can play much better but I'm happy.
"We started the tournament with three points and it's very important."
The sizzling heat in Frankfurt appeared to take a heavy toll on England's players, and the South Americans coped better and looked fitter than Eriksson's men in the latter stages.
"Maybe we suffered a lot. I think this was a real hot, hot day and I think that knocked us in the second half," Eriksson added.
"But most important was the result today, we were suffering but it's a very good start."
Eriksson said decision to take Michael Owen off early in the second half, to be replaced by Stewart Downing, was purely tactical.
Joe Cole occupied a role just behind Peter Crouch after Owen's withdrawal, with Downing playing on the left.
"I thought we were finding it difficult to keep the ball so I tried to have a player who could link the ball up a little," said Eriksson.
"Joe Cole did very well.
"I think it got better at the end."
Eriksson refuted the suggestion that taking off Owen caused England's performance to fade.
He added: "No, I think we lost rhythm, I think we started the second half poorly.
"I don't regret what I did when I picked the team, If you can find better players than Owen and Rooney I can't.
"I changed Michael because we wanted to see some fresh legs. I think Michael did well today. He will be better every game now."
Meanwhile, Paraguay coach Anabal Ruiz claimed England had the strength to go all the way to the final.
He said: "I think we handled the heat better than they did and were superior physically.
"From the 15th minute we controlled them. They are a good side but we were up at their level. England are a very strong team but after the surprise of the first goal we managed to control a strong team who could go to the final game."
He was also optimistic that Paraguay could still qualify for the knockout phase.
Ruiz said: "We're capable of getting two good results and going on to the next round."