After coming back from a two-game suspension, the striker started the match and scored what turned out to be the winning goal as Roy Hodgson's men put in a somewhat shaky display against the co-hosts.
And the Manchester United man believes that by finishing top of Group D and earning an extra day's rest by playing in the fourth quarter-final on Sunday, the Three Lions are in good stead for the rest of the tournament.
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"I think we know our qualities and what we're capable of," Rooney told ITV. "We've got together and worked really hard, we've done a lot of tactical play in training and we're difficult to beat.
"I don't think there is any team that would fancy playing us, we're difficult to break down and we've got the players who can score goals, so it's going well at the minute. We'll get a good rest now and hopefully we'll be back fresh."
Having not scored a goal in a major tournament since Euro 2004, the 26-year-old headed home from close range to set up a last-eight clash with Group C runners-up Italy.
"[I am] Obviously delighted with the win and to score is obviously great. I haven't scored in a major championship for a while so it was nice to get the goal that effectively won us the game," he added.
"I thought the whole team were fantastic, we defended really well and stuck in there at times against a difficult crowd, I thought our fans were brilliant as well and we deserved the win."
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"I said before it doesn't matter [who England play], the main thing was to get through the group and to finish top is great for us. We play Italy now so it'll be a difficult game of course but we're confident, we believe in ourselves and you never know," he continued.
"We stuck together, we have a belief in ourselves and are ready for the challenges ahead."
The striker gestured towards his hair when celebrating his goal and added: "I used a bit of Andy Carroll's product before the game and he asked me to do it if I scored a header. Hopefully I'll end up with hair like him."
The game against Italy on Sunday kicks off at 20:45CET in Kiev.