Rooney scored twice after Alex Oxlade-Chamberlain had headed the visitors in front, with Andrew Robertson scoring Scotland's consolation.
And the Manchester United striker declared his happiness with the way England dealt with a partisan home crowd.
"It's a great victory for us," he said. "We spoke about the atmosphere before the game and it was terrific. We had to show our character.
"Scotland started quickly but we showed our ability with the ball and our mental strength. After we scored the first goal I thought we controlled the game.
"When Scotland got their goal back it could have been a bit edgy, but we responded fantastically. It was a great victory and a great performance.
"That game is great for the fans and fantastic to play in - it's not my decision but it'd be great for us to play more games like this.
"It was very special for me, to score two goals for England in Scotland at Celtic Park."
Rooney's brace saw him surpass Jimmy Greaves to go outright third on England's all-time goalscoring list, also moving within two of second-placed Gary Lineker.
The 29-year-old's tally now stands at 46, with Bobby Charlton topping the standings on 49.
"I'm enjoying my football," he added. "I've always loved playing for England, I'm on a good run of goals and I hope that continues.
"If that means I break the record then I'll be delighted."
