Wales’ 3-0 win over Russia in Toulouse meant the Three Lions finish second in Group B.
Slovakia must now wait to see if they qualify as one of four best third-place best teams after their goalkeeper Matus Kozacik pulled off a string of saves – some more luck than judgement.
England will now play their last 16 game in Nice next Monday against the side who finishes second in Group F, most likely against Hungary or Portugal.
Slovakia coach Jan Kozak kept faith with the starting side which beat Russia 2-1 last Wednesday.
Vardy worked hard throughout, but squandered two clear chances of England’s nine first-half attempts on goal to Slovakia’s single effort.360Verdict:
The England manager keeps telling everyone how well they are playing but they have drawn with Russia and Slovakia (both beaten by Wales) and sneaked past the Welsh with a stoppage time goal.
Man of the Match: Martin Skrtel (Slovakia)
Slovakia came to defend and their captain led by example. He crucially cleared Alli’s effort off the line, organised the troops and made countless blocks and tackles to frustrate the English.