Roy Hodgson has played down concerns England may face stronger opposition after finishing second in Group B and told ITV: "I'm not frightened of anybody."
England ended the group stage behind Wales after a frustrating goalless draw against Slovakia in Saint-Etienne on Monday.
They had been dominant in all three group games but only managed to beat Wales, having drawn 1-1 against Russia in their opener after conceding a late equaliser.
As a result, Wales will play the third-placed team from either Group A, C or D, while England will play the second-placed team in Group F -- which contains Hungary, Iceland, Portugal and Austria -- in Nice next Monday night.
"Finishing second in the group is a disappointment because we'd have liked to have won it," Hodgson said. "But we're still in the last 16 and who's to say the team we'll play by finishing second is going to be that much stronger than the team we would have played that's finished third? You just don't know that.
"The way we're playing at the moment to be quite honest I'm not frightened of anybody that we would play."
Hodgson admitted it was frustrating to have only taken five points from the group despite having been on the front foot throughout the majority of the matches.
"Well, it's like that when you dominate three games like we've done and only manage to win one of them," he said. "The fans were magnificent again today and it's a real disappointment for us we haven't been able to give them a win, but I've got to say I don't think we can do too much more than we did.
"We dominated the game from start to finish and had so many attempts and so many chances as well really, and one day we're going to put those chances away.
"As far as I'm concerned I can't fault the effort and the work that the lads put in. It's a little bit embarrassing I think that we've played three games now and in each of the three games it's been attack versus defence.
"I actually never thought I'd see an England team in a tournament be able to dominate three games as much as we've done so that gives me some sort of satisfaction.
"I'm pretty sure that sooner or later we're going to make somebody pay because if we keep dominating and creating chances like we do we're going to score goals one day."
Hodgson made six changes to his starting lineup on Monday, resting captain Wayne Rooney and star performer Kyle Walker as well as the right-back's Tottenham teammates Dele Alli and Harry Kane.
The decision appeared to have been an attempt to give some of his key players a rest, with former England skipper Steven Gerrard having noted before Euro 2016 that he had always felt exhausted in the latter stages of international tournaments.
Hodgson said: "If you don't win the game people can always say the team selection's wrong. I'm used to that one. We brought players on. I thought that was useful to be able to do while Slovakia were tiring. I thought we kept up our domination by bringing on people like Dele Alli, Harry Kane and Wayne Rooney.
"I'm not so certain it would have made a vast difference from the start because we'd still have been playing against this team with 11 men in defence and we'd have still been battling away to try and find that opening."
He added at his news conference: "What would have changed had Wayne Rooney started? Are you saying he would have scored the goals the others missed?
"We finished the game with Wales with Daniel Sturridge and Jamie Vardy up front and everyone was saying they were very positive changes."