A much-changed England had to settle for second spot in Group B as Slovakia clung on for a goalless draw which may also see them progress at Euro 2016.
Roy Hodgson made six changes from the side that started the 2-1 win over Wales last time out, but will face criticism after England drew a frustrating blank in Saint-Etienne while Chris Coleman's side thrashed Russia 3-0 to win the group.
Jamie Vardy and Daniel Sturridge, the goalscoring heroes against Wales, were given starts, with Wayne Rooney among those rested as Gary Cahill was handed the captain's armband.
Vardy and Sturridge were among a number of players guilty of missing opportunities as England failed to make their dominance count at the Stade Geoffroy-Guichard, where they suffered a World Cup last-16 exit to Argentina in 1998.
Slovakia, to their credit, produced a dogged rearguard action to keep Hodgson's men out despite spending long spells camped in their own box and will likely go through as one of the best third-placed sides.
England looked to control possession and set the tempo from the start, with Vardy flashing an improvised effort just over the crossbar from a tight angle early on.
The Leicester City striker then flicked on Jack Wilshere's cross for Sturridge inside the six-yard box, but Peter Pekarik made a crucial block.
Adam Lallana escaped down the left in the 16th minute and provided a delivery that initially eluded Jordan Henderson, who managed to shoot on the turn but saw it deflected behind for a corner that came to nothing.
Goalkeeper Matus Kozacik came to Slovakia's rescue moments later, thwarting Vardy after he raced through one-on-one beyond the attentions of a labouring Martin Skrtel.
Slovakia, who lost to Wales before beating Russia, were hanging on at times and the impressive Nathaniel Clyne got the better of Tomas Hubocan again before picking out Lallana, whose powerful first-time effort was beaten away by Kozacik.
Jan Kozak's men showed a little more attacking intent early in the second half and Pekarik won a free-kick that Joe Hart had to tip away from the onrushing Marek Hamsik, before England escaped unharmed from a mix-up between the goalkeeper and Chris Smalling.
Rooney was summoned from the bench before the hour to rapturous applause and Dele Alli followed soon after, handing England fresh impetus as the Tottenham midfielder immediately had a shot cleared off the line by Skrtel.
England came close again when Sturridge needed only to make meaningful contact with Eric Dier's lofted pass in order to break the deadlock 17 minutes from time, but failed to do so before being replaced by Harry Kane.
The Spurs striker flicked a late header wide as England continued to press for a winner that never came, leaving the likelihood of a much tougher last-16 tie than might otherwise have been the case.