A heavily rotated England were held to a frustrating goalless draw by Slovakia in St Etienne on Monday and enter the Euro 2016 knock-out phase as Group B runners-up behind winners Wales.
England, with six changes made from their win over Wales, dominated proceedings but a host of missed chances proved their undoing against a Slovakia side which offered next to nothing but clung on to claim a point.
Slovakia keeper Matus Kozacik was the man of the match with fine saves denying Jamie Vardy and Adam Lallana in the first half while Martin Skrtel cleared Dele Alli's shot off the line in the second.
Wales defeating bottom Russia 3-0 elsewhere means they top the group on six points with England second on five. Slovakia have four and must hope they are one of the four best-ranked third teams to progress.
Britain's Prince William was in attendance and saw Hodgson send out a team with several changes, including Jack Wilshere for Wayne Rooney, from the previous outing. Vardy and Daniel Sturridge, scorers off the bench last time, were included from the start.
"It's certainly very disappointing that once again we've had all the play, lot of opportunities around the Slovakia box and not been able to take one, so I can't deny that's not disappointing," Hodgson said. "But I believe that will come, we have players in the team who can score goals.
"We should have won, everything we did on the field led to us being able to win."
England were immediately on top as Peter Pekarik denied Daniel Sturridge a tap-in before Adam Lallana and Jordan Henderson both fired wide.
Vardy raced beyond Skrtel onto a long ball only to shoot straight at Kozacik and the keeper was again sharp to palm away Lallana's shot after great work by Nathaniel Clyne.
"We knew they are an attack-minded, top quality team, they proved it during the match," Kozacik said. "They pressed us but luckily we didn't concede. We managed to hang on and get the point."
Slovakia offered absolutely nothing in the first half with star player Marek Hamsik of Napoli totally anonymous in the middle of the park.
After the break a miscommunication between Chris Smalling and Joe Hart almost presented Robert Mak with a rare chance but normal service was soon resumed. Clyne, released by a brilliant Sturridge pass, fired off the hip of Kozacik.
"I think their line-up was quite attack-minded, we were pressed deep and we tried to get that point," coach Jan Kozak said. "It was a very important point to try to get through to last 16.
"Kozacik put in a great performance, he has been performing consistently in the national team. He's a very honest, hard-working goalkeeper and I'm happy for him."
Rooney was introduced for Wilshere on 56 minutes and soon after Alli joined him replacing Lallana. With virtually his first touch Alli seemed to have turned in Henderson's cross only for Skrtel to clear off the line with Kozacik beaten.
Eric Dier, who was one of England's best players having strolled through the game in a holding midfield role scarcely breaking sweat or wasting a ball, nearly found Sturridge with a clever chip but the striker failed to connect.
That was Sturridge's last action, as he was pulled for Harry Kane with 15 minutes remaining.
England continued to push for the opener, against a Slovakia side which had long since given up the pretence of trying to do more than hang on for a point.
Rooney was energetic but though he had nice touches, failed to threaten often and dragged his only attempt on goal well wide.
England were given five additional minutes in which to find a winner but Slovakia held on to claim their scarcely deserved point.