Denmark and Slovenia joined group winners England in qualifying for the Euro 2024 last 16 on Tuesday from a turgid Group C, where Serbia ended up the fall guys along with Croatia from Group B.
Denmark drew 0-0 with Serbia to eliminate the bottom side and snatch second spot from third-placed Slovenia, who also played out the goalless stalemate with England they needed to reach the knock-out stages at a major tournament for the first time.
After three draws, Slovenia had the exact same record as Denmark but finish below them because of fair-play rankings.
But they are guaranteed to be one of the four best third-placed teams given they finished with more points than now eliminated Croatia and have a better goal difference than Hungary.
England, who had already qualified for the last 16, finished top but it was another dour performance from the pre-tournament favourites.
"It was a tough game. I thought we played a lot better than the other two games, better on the ball. Just that little bit of the quality in the final third (was missing)," captain Harry Kane told ITV.
"We've stepped it up in the knock-outs in past tournaments. It is going to be a difficult challenge ahead."
England will play a third-placed side from Groups D, E or F on Sunday while Slovenia, who have never won a game at a Euros, must wait to have their opponents confirmed but look set to meet Portugal.
Denmark face hosts Germany on Saturday.
"Anything is possible," said Denmark defender Jannik Vestergaard. "We need a top performance, and maybe Germany don't reach their best level - but it's definitely doable."
Only one game at these Euros had previously ended 0-0. Group C finished up with just seven goals in total, fewer than hosts Germany netted themselves in the group stage.
Denmark came closest through the excellent Man of the Match Christian Eriksen and Vestergaard against Serbia in Munich. But knowing a draw would get them through, they lacked the urgency to push for a winner.
Dragan Stojković's side, who almost scored late on through Aleksandar
Mitrović, needed a win to progress but instead are heading home in their first Euros as solely Serbia.
England midfielder Conor Gallagher, in place of Trent Alexander-Arnold, was the only new starter compared to the lacklustre 1-1 draw with Denmark, despite a widespread English media outcry for bigger changes.
Slovenia's much-hyped striker Benjamin Šeško had an early header easily saved in Cologne while England were almost as plodding and predictable as against the Danes in the first quarter.
The Three Lions momentarily burst to life when Bukayo Saka tapped in but Phil Foden was flagged offside with the assist.
They then got further forward than against Denmark as they came up against the low block of Slovenia, who have never beaten England, but it was still dire stuff.
Foden, previously criticized more than most England players, was one exception and he tested goalkeeper Jan Oblak with a free kick - but there were still boos again at half-time.
Gallagher was replaced by Kobbie Mainoo at the break and the Manchester United teenager made a positive difference but not enough to force a goal.
England fans started singing loudly in the second half to try to boost their players but also to no avail, although substitutes Cole Palmer and Anthony Gordon shone and Declan Rice blasted wide.
Defender John Stones said: "I understand some of the fans' frustration with us not scoring. The subs made a great impact today, credit to them. Especially Cole made some great chances for us."