The stalemate means England have drawn two and won one of their matches in the competition, ending with five points while Slovakia are third on four.
Slovakia 0-0 England
UEFA Euro 2016
Group B
Stade Geoffroy-Guichard, Saint-Etienne
Monday 20 June 2016
But although Wales thumped Russia 3-0 to top the group with six points, Hodgson is adamant the style of football his side is playing will soon change their fortunes.
The England manager said: “We’re frustrated, but it’s like that when you dominate three games and only manage to win one of them.
“The fans were magnificent again today so it’s disappointing not to be able to give them a win but I don’t think we could’ve done any more than we did.
“We dominated the game from start to finish and had so many attempts and chances and one day we’re going to put those chances away.
“As far as I’m concerned I can’t fault the effort and work the lads put in. It’s a little bit embarrassing that we’ve played three games and in each of the three games it’s been attack versus defence."
England's Jamie Vardy races past the Slovakia defence in Saint-Etienne
The Three Lions controlled 60 per cent of the possession and had 29 shots on goal against Slovakia but could not break the deadlock at the Stade Geoffroy-Guichard.
Hodgson added: "The way we’re playing at the moment – to be quite honest – I’m not frightened of anybody.
“I thought I’d never 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.
“And 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’re doing we’re going to score goals one day.”
England will play the runners-up of Group F in Nice on Monday – meaning they will face one of Portugal, Hungary, Iceland or Austria in the last 16.
Hodgson added: “Finishing second in the group is a disappointment as we’d have liked to have won it but we’re still in the last 16.
"And who’s to say that the team we play by finishing second will be that much stronger than the team who finish third – you don’t know that."
