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.
Hart turned in a strong performance in a 1-1 draw with Chelsea last weekend, but the former Blues striker said Monday night's display showed the 30-year-old lacks the consistency required of an global goalkeeper.
But West Ham refused to lie down and Carroll, missing for the last 13 games through injury, showed his quality when Cresswell delivered a ideal ball into his path and the former Liverpool forward fired an unstoppable volley past Butland. Instead it was another substitute, Andy Carroll, who had the final say, lashing in a 90th-minute equaliser to spare West Ham an ignominious result. In his mind, he is free and just enjoying the game.
It certainly took a while before there was anything to liven up the atmosphere. They are still looking for points as well.
Initially, however, the former Everton, Sunderland and Manchester United boss was anxious he would not be able to coax the best form out of Arnautovic, who had struggled in his first four months at the club, often being criticised for his poor work-rate.
West Ham were searching for back-to-back Premier League victories at the London Stadium for only the second time and threatened within the opening moments as Stoke goalkeeper Jack Butland repelled Arthur Masuaku's low drive with his feet. Southgate at this stage had little to see as Butland and Hart were largely untroubled.More news: GOLDOC boss Beattie apologises for closing ceremony 'stuff-up'
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Stoke managerLambert, meanwhile, remains convinced that his players have the quality to prolong the club's 10-year stay in the top flight, with Sunday's clash with Burnley now heightened in importance.
- On home soil, West Ham have lost just one of their last seven top-flight games (W3 D3), after losing three of the six before that (W1 D2). If Stoke are relegated, Xherdan Shaqiri will be in high demand during the summer transfer window.
It was the third goal they had ruled out in the game. Stoke have not managed two goals in a league fixture since beating Huddersfield 2-0 in January.
The other subplot to the evening was that this was Michael Oliver's first game as a referee since the now-infamous Champions League tie between Juventus and Real Madrid, Gianluigi Buffon's red card and all the unpleasantness that has followed.
"I think the ref the decisions right from what I have heard".
Butland was then on hand to turn an Aaron Cresswell free-kick around the post, while the England stopper also took a Marko Arnautovic shot flush in the face.