Joe Hart won his 62nd England cap with manager Roy Hodgson making six changes from the team that started against Wales.
That meant Raheem Sterling started his night on the bench as England looked for the point that would guarantee them a place in the last 16 of the competition.
England began brightly and Jamie Vardy’s flicked header almost allowed Daniel Sturridge to open the scoring but the former City striker was denied by a last-gasp tackle.
Then Vardy raced clear on 17 minutes but fired his shot straight at the Slovakian keeper who beat the ball away to safety.
The dynamics of the game shifted early on with the news that Wales had already opened up a 2-0 lead over Russia, though that put more pressure on Slovakia than it did England, so long as the scores stayed level.
With three former members of City’s 2008 FA Youth Cup-winning team in Robbie Mak, Vladimir Weiss and Daniel Sturridge on the pitch, England continued to knock on the door with Adam Lallana denied by another Kozacik save on 33 minutes.
Jordan Henderson saw a powerful shot bravely blocked by Durica just before the break but the teams went in level at the break.
Hart was finally called into action on 52 minutes when he palmed a dangerous cross on its way, but a poor cushioned back pass fell short and Mak almost nipped in to score but Hart did enough to distract the Slovakian.
Three minutes later and another ex-Blue came close as Weiss hit a low shot that Hart saved comfortably down to his right.
Sub Dele Alli saw a shot scrambled almost off the line shortly after coming on, but still England couldn’t find the goal their overall play merited.
Slovakia defended in numbers, frustrating England and the 30,000 fans backing the Three Lions as the clock ticked down.
There was to be no dramatic late winner on this occasion and England will now face the runner-up of Group F, which will be one of Austria, Portugal, Iceland or Hungary on Monday 27 June in Nice.
