Rooney hailed what he believes are "good times" for England.
"We knew it was going to be a tough game, they had a couple of breaks and could have scored, but we played some great stuff in the first and second half," he told ITV.
"Getting the goal gave us some belief, the confidence to go on. We believed we could win and then Stevie's goal has seen us qualify."
The Manchester United man added: "A big part of our preparation was being patient. We knew we may even have to win the game in the last 10, five minutes. We kept our focus and deserved to win.
"We always remained positive no matter what was said. We had a great focus and belief going into these two games. That came out.
"We have some fantastic young players, experienced ones like Steve, Frank (Lampard) and me, we have a good blend, are looking forward, excited and these are good times for England."
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