Manchester United striker Rooney did not have a single shot on goal.
Hodgson said: "No, but he did a lot of good things.
"He was very much involved in most of our attacking play. I was satisfied with his performance.
"I have to accept we do have a lot of firepower unavailable to us at the moment.
"We just have to hope it's with us for the World Cup qualifiers in September.
"I'd be hard pushed to say too much negative about the players in our team.
"There weren't many negatives, other than that we didn't win the game.
"The opponents put a spanner in the works and the Irish did that very well."