Eriksson expressed satisfaction at his team's opening 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 told BBC1 that the 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."
Beckham blamed England's fading performance on the heat rather than the manager's decision to take off Owen.
The skipper, who played a crucial part in the early winner, said on BBC1: "You don't realise how hot it was out there.
"We were good at times but we gave away the ball too much. But it was hot and we got what we wanted. That was a good start and we have the three points.
"The performance could be better but we will work on that. We set out to get the three points and we did that.
"We let them (Paraguay) pass the ball around too much.
"But we were exhausted. We can put it down to that because we are usually strong and our fitness levels are high."
Looking ahead to the next match, Beckham predicted a later kick-off - 6pm (5pm BST) in Nuremberg on Thursday - might suit England better.
"We will be alright. This was a three o'clock kick-off and is right in the middle the day. It was 28 or 29 degrees out there," he said.
"We must perform better better and play better but we got what we wanted."
He added: "I don't think we lost our shape too much after Michael had gone off and South American teams play the ball through well."
Midfielder Frank Lampard stressed the result was more important than the performance.
He told BBC1: "The heat sapped us a bit in the second half - but to get three points in our first game is the important thing.
"We know we can do a bit better but we've got a bit of time to work on things - and we'll get better.
"Once the dust settles we'll see what an important result this is."
He continued: "We started really well with great intentions, moved the ball really well and got a goal.
"We were upset at half-time we hadn't got another.
"Paraguay are more used to this climate and we sat back a bit and suffered under pressure - but we defended well and that's a big plus for us today."
Chelsea midfielder Cole, who was taken off with eight minutes remaining, is hoping for cooler weather for England's remaining games.
"It was hotter than Portugal (during Euro 2004)," said Cole on BBC Radio Five Live. "We'll be praying for some cold and damp weather over the next few weeks. Evening kick-offs will help us."
Cole was pleased with getting three points from a tricky game, adding: "I think we did finish them off - we have three points in the opening game.
"There were huge expectations and, coupled with the weather, it was a good performance, especially in the first half, and a fighting performance in the second half.
"I don't think they had many chances, it was a good performance. Now we can look forward to Trinidad and a win should get us through."