England, who had already qualified for the round of 16, ended the group stage with five points but it was another desperately disappointing night for Gareth Southgate's side who have managed only two goals in three games.
While the final whistle sparked joy in the Slovenian ranks, many England fans left before the end and showed their frustration by booing the players.
Slovenia defended superbly to hang on for the draw, which meant they finished with three points in third spot, the same as second-placed Denmark, who were held to a 0-0 draw by Serbia.
Although they had the same goal difference, goals scored and disciplinary record, the Danes advanced in second place above Slovenia due to their UEFA ranking and will face hosts Germany.
The tie breaker was who had the best qualifying record - and Denmark edged Slovenia on the head-to-head after both sides also finished on the same points in the qualifiers.
England, despite 71% possession, managed only three shots on target and while they move into the last 16 as group winners, they will need a drastic improvement to go one better than Euro 2020 when they were beaten by Italy in the final.
MUGGY NIGHT
England's fans were in full voice as kick off approached on a muggy night by the Rhine -- buoyed by other results that meant European heavyweights France, Germany, Spain and Portugal have all ended up in the other half of the knockout round draw.
England knew a win would guarantee avoiding an early showdown with those sides but by halftime many of their fans had disappeared for refreshment with their team again toiling as an attacking force against a well-drilled Slovenian outfit.
Bukayo Saka did have the ball in the net after 19 minutes but Phil Foden was offside before playing in a low cross.
An overly deliberate England had to wait until the 31st minute to register their first effort on target -- captain Harry Kane firing in a shot that was easy for goalkeeper Jan Oblak.
Oblak also had to be alert to deal with a Foden free kick but Slovenia, bidding to reach the knockout phase of a major tournament for the first time, were relatively comfortable.
Kane was inches away from converting a Kieran Trippier cross just before halftime but Slovenia also showed ambition with the lively Benjamin Sesko heading an early chance straight at keeper Jordan Pickford.
Midfielder Kobbie Mainoo appeared for the start of the second half in place of Conor Gallagher who had replaced Trent Alexander-Arnold in the starting lineup, Southgate's only change from the first two games.
England took a stranglehold in the second half with 80% of the ball as Slovenia camped in their own half, but clear chances remained elusive.
Cole Palmer, who scored 22 Premier League goals for Chelsea last season, came on to huge cheers in the 70th minute and immediately gave England some much-needed spark.
Palmer forced Oblak into a save in stoppage time but Slovenia showed incredible resolve to stand firm and send their fans into delirium with a vital point to progress.
