However, the West Ham boss believed his side should have wrapped the game up long before the late drama.
That strike spared the blushes of Hart, whose fumble allowed Peter Crouch - another second-half substitute - to put Stoke ahead in the 79th at the Olympic Stadium.
And despite the draw edging West Ham closer to safety, Carroll insists no club is safe.
"The goal was a kick in the teeth", Crouch said.
Hart appears set to be included in Gareth Southgate's England squad for the World Cup despite playing second fiddle to Adrian for much of the Premier League season.
Whether Hart makes it to Russian Federation is still open to debate.
The errors won't help Hart's chance of regaining the England jersey off Jordan Pickford ahead of the World Cup in Russian Federation - if he is included in the 23-man squad for the tournament, that is.
The change paid off for the Hammers as Carroll secured the equaliser in the 90th minute with a fine first-time finish into the bottom corner to deny the Potters three priceless points in their fight against relegation.
But unless they have a turnaround in fortune in the final four games, he will not have many chances to extend that record.
Meanwhile, Stoke chief, Paul Lambert, said: "If we'd got the three points, I thought we'd deserved something from the game anyway. Regardless of how we do it, we have to get a win but we certainly will drag teams into it".