In other results on Thursday (Friday AEDT), Erling Haaland became Norway's record scorer at the age of 24 with a double in his country's 3-0 win over Slovakia in Oslo, while France - playing without Kylian Mbappe and the retired Antoine Griezmann - beat Israel 4-1.
After leading England to back-to-back victories since becoming temporary coach after the European Championship, Carsley felt emboldened enough to field a team without a recognised striker in the absence of injured captain Harry Kane.
The line-up looked exciting on paper but resembled a mess on the field as Greece repeatedly picked off England and got in behind a stretched defence.
Vangelis Pavlidis scored the opener for the visitors at Wembley Stadium in the 49th minute, Jude Bellingham equalised in the 87th, only for Pavlidis to take advantage of more sloppy defending to grab Greece's winner in the fourth minute of stoppage time.
Greece's Vangelis Pavlidis certainly rose to the occasion with a double against England. (AP PHOTO)
Greece's players, who also had three goals disallowed in the game, celebrated one of their most famous wins by gathering together and holding up the No.2 jersey of George Baldock, the Panathinaikos defender found dead in his Athens home on Wednesday at age 31.
British-born Baldock played 12 matches for Greece and there was a period of silence in tribute to the right back ahead of the game, with players wearing black armbands.
It was England's first loss to Greece, ranked No. 48 in the world ranking, in 10 matches between the teams and deals a major blow to Carsley's hopes of becoming coach on a permanent basis.
It was meant to be fluid set-up, with in-form Chelsea playmaker Cole Palmer starting a competitive international for the first time for England and deployed in central midfield, with Phil Foden and Bellingham splitting time as the furthest player forward. It didn't work.
Jude Bellingham's goal wasn't enough to stop England losing against Greece. (AP PHOTO)
Carsley insisted the selection was not an "experiment".
"We never really gave ourselves a chance to see whether it was the right decision or wrong," he said.
"With the players we've got, we've got to be courageous at times with our systems and be creative. I thought it was important to try something different."
In Budapest, Mbappe wasn't called up by France because of a minor injury, even though he has since played for Real Madrid, while the surprise retirement of Griezmann gave it the feel of a new era for Les Bleus.
Goals by Matteo Guendouzi in the 87th minute and Bradley Barcola in the 89th wrapped up France's win against Israel, after Eduardo Camavinga and Christopher Nkunku netted in the first half.
In Oslo, Haaland scored twice to move to 34 goals for Norway, one more than Jorgen Juve from the 1930s.
Erling Haaland (left), who was captaining the side, scored a double in Norway's win over Slovenia. (AP PHOTO)
Haaland was captaining Norway for the first time in his 36th international appearance.
Alexander Sorloth also scored for Norway.
In Rome, Italy forward Lorenzo Pellegrini's red card proved decisive as his team squandered a two-goal lead and drew 2-2 with Belgium.
Italy went in front after barely 60 seconds through Andrea Cambiaso, before striker Mateo Retegui made it 2-0 in the 24th minute.
Pellegrini was sent off for a foul on Arthur Theate in the 40th minute. From the resulting free kick, Maxim De Cuyper tucked away a fine finish from a well-worked move, before Leandro Trossard equalised in the 61st minute.
In other results, Moldova beat Andorra 2-0, North Macedonia scored a 3-0 away win over Latvia, Gibraltar pipped San Marino 1-0, Ireland defeated hosts Finland 2-1, Austria routed Kazakhstan 4-0, and the Faroe Islands and Armenia fought out a 2-2 draw.
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