Roy Hodgson's men were in action for the first time since their winless World Cup campaign in Brazil, and they were unconvincing in London - a Rooney penalty with 22 minutes remaining splitting the sides.
The Manchester United striker, who came off shortly after scoring for now-former club team-mate Danny Welbeck, said England had plenty of scope for improvement.
"I thought I could have done better – we all could have done better," Rooney told ITV Sport.
"It's the first game after the World Cup and it was important that we got the win tonight, especially going into the game on Monday.
"In the first half we moved quite well but they made it difficult for us; sat back and created a few opportunities.
"In the second half we started really sloppily and that was disappointing, as we wanted to go out and really take the game to them.
"We got the win in the end and there are a lot of young players in this team. They are still learning."
England open their Euro 2016 qualifying campaign against Switzerland in Basel on Monday.
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