West Ham boss David Moyes cut a serene figure after a last-gasp leveller from substitute Andy Carroll boosted his side's Premier League survival chances and deepened the relegation worries of opponents Stoke.
Hart has already lost his place as England's No 1 and, at this rate, he must be in danger of being cast adrift from the squad that Southgate takes to the World Cup in Russian Federation this summer.
"For the team, for us, at the time it was hard because it meant we had to go and look to change after we had been the dominant team, apart from the first five or 10 minutes of the second half".
"You can not take someone because they are a nice bloke and good in the dressing room", Sutton said on BBC Radio 5 live.
He said: "I tried to bring it down and it did hit my hand but it was because of a shove which might even have been a penalty".
But West Ham showed all their fighting qualities as they rescued a point in added time when Carroll volleyed a cross from Aaron Cresswell past Jack Butland into the corner of the net. We've had some really good games and we've just been really unfortunate with Lady Luck. I think the important thing was to make sure we didn't lose tonight. "I can't fault the effort or commitment, and we'll see what happens".
"I'm keeping my target high and I'm hoping to win ten games. If we have 40 I think it's a lot to ask the teams below us to get it".
"That's why we had to find something which meant that maybe he wasn't quite as exposed to having to double-up, help the full-back out", Moyes said. "It is tough at the minute but we'll keep working".
A free-kick fell to the home side six minutes later after a foul near the edge of the box.
The Mexican worldwide has scored eight goals this season, including four in his last eight games. Oliver had a steady night - a nice change, presumably, from being told he has a "dustbin for a heart" - and his assistant got the big decisions right.