The 28-year-old scored the only goal in the uninspiring win when he struck from the penalty spot in the 69th minute.
Just 40,181 turned up to the national stadium to watch Roy Hodgson's side in the friendly match - the lowest England crowd at the new Wembley by more than eight thousand.
Following their disappointing World Cup campaign where they exited at the group stage, Rooney admitted his performance had been lacklustre.
"I thought I could have done better. We all could have done better," Rooney told ITV1.
"It's a night, 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 and sat back and created a few opprtunities in the first half.
"In the second half we started really sloppy 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 and we will learn. They are still learning."
England face Switzerland in a Euro 2016 qualification match on Monday.
England manager Hodgson took positives from the way his young side responded to a change in approach midway through the second half.
He said: "The injection of pace of Danny Welbeck, Fabian Delph and (James) Milner and a slight change in the system we got back on top again and started to create chances.
"In the end I thought we were good value for our victory.
"The good thing with the players we have at the moment, and there were three out there making debuts today, is that many are playing early matches in their international career and it's good that we have these options.
"We definitely changed the way we were playing in terms of system with about 20-25 minutes to go and I thought that worked well too when Welbeck came in behind Sturridge.
"I thought that got us going as well and in the end with a little bit of luck we would have aggravated the score. The important thing was the victory."
Despite his positive outlook, Hodgson knows there is plenty still to work on.
"We started the second half poorly and I was disappointed by our first 10-15 minutes at the start of the second half and Joe (Hart) had to make a couple of saves having been pretty much a bystander in the first half but luckily we got ourselves going again," Hodgson added.
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