Roy Hodgson made six changes for the final group game, with captain Wayne Rooney among those to drop out for Jordan Henderson following a last-gasp victory over Wales on Thursday.
Jamie Vardy, Daniel Sturridge, Jack Wilshere, Nathaniel Clyne and Ryan Bertrand were handed their first starts at the France finals, but England could not find a way past a determined Slovakia side.
A draw for the Three Lions ensured they qualified from Group B, but Wales' 3-0 win against Russia to top the group means England now face a potential last-16 encounter against Portugal should Cristiano Ronaldo's side also qualify.
England started the tournament in disappointing fashion as a late goal cost them a win against Russia, but Sturridge scored a dramatic injury-time winner against Wales to tee up Hodgson's side for the final group game.
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