The Three Lions held off the defending champions until the 85th minute, before Enzo Fernandez cannoned home Messi's pass, and the iconic captain then delivered a perfect cross for Lautaro Martinez to head home the winner.
Thomas Tuchel's decision to throw on three extra defenders - as England looked to hold a 1-0 lead - has come under major fire, as his game plan was undone by Argentina's all-star attack.
Despite the failure to make the final, Tuchel's job is expected to be safe, but former England star Michael Owen has launched a withering critique of his approach.
"Dropping back and putting 11 men on the edge of your own box, and then just heading it wherever or kicking it as far as you can, that's not brave - it's the opposite," he told BBC Sport.
"Football isn't about getting a bloody nose and everyone saying that's fantastic, it's rubbish.
"I can get my local pub team to do that and that's why we (England) lost out in this World Cup.
"Celebrating that win over Mexico in the way we did was wrong. As a player, the minute that happens, you start to think 'we've won.' Subconsciously, when you go 1-0 up - what are the players going to think?
"Then the manager brings on three defenders. What message does that send to Argentina?"