Although Thursday's victory booked them into the World Cup second round, England's profligacy in front of goal meant they had to wait until the 83rd minute for Peter Crouch to break the deadlock. Steven Gerrard got the second in stoppage time.
"We showed a lot of patience, it's always difficult against a team who defend with nine or 10 men behind the ball every time they lose it," Eriksson told a news conference.
But he added: "If you don't take the chances when you create them, it will always be like this.
"If we'd taken those chances we created in the first half or early in the second half, it might have been a different match."
Defending their performance against the smallest nation at the finals, Eriksson said: "If we play one of the big teams in this tournament, it will not be a match like that.
"It will be completely different and we will be better and better.
"Wins give you more confidence," he said, referring to last weekend's 1-0 victory over Paraguay in their group opener.
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Man-of-the-Match Beckham, who provided the cross for Crouch's goal, was on the same wavelength.
"We knew we could always create chances -- and if we'd taken our chances we'd have been a few up before then," he said of the Crouch's opening goal.
Asked if it was a good England performance, Beckham said: "It was a performance of togetherness, not our best performance but one where we all had to dig in.
"We know we can do better than this and we know that there's better to come. The most important thing is two games and six points."
England face Sweden in their last group game on Tuesday in Cologne.