West Ham arrived here on a quest for the victory that would have lifted them to third in the table but they ended up relieved to take a point. They did not deserve more. Nor did Aston Villa, and that was frustrating for the hosts, who spent the last portion of the game mostly failing to trouble 10 men after Arthur Masuaku was sent off.

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Nearly all the home players threw themselves to the ground at the final whistle: this was an opportunity missed. Dean Smith has said since the start of the campaign that he expects home wins to form their basis for surviving, maybe even thriving, in the Premier League. So being unable to punish West Ham here hurt.

While Villa lacked precision when it mattered most, there could be no questioning their desire – at least not after an extraordinary incident in the first-half between Anwar El Ghazi and Tyrone Mings. When the defender lambasted the midfielder for not tracking back hard enough, El Ghazi responded by pushing his forehead into that of his teammate in what could easily have been construed as a headbutt, albeit not a hard one. At least the referee, Mike Dean, remained level-headed and, after a review by VAR, he let El Ghazi off with a lecture. Smith said that, while El Ghazi was out of order, his players dealt with it so well that he did not have to address it at half-time.

“I didn’t need to,” said the Villa manager. “There’s great togetherness in the dressing room. El Ghazi went over the edge of what we want and the players dealt with it swiftly. I’m happy for them to do that. We’re playing a team sport, it’s competitive and there’s heat-of-the-moment things that happen. It got dealt with very quickly. El Ghazi has a little bit of red mist in him, like most professional footballers.”

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There was no such forgiveness for Masuaku in the 67th minute, however. Already on a yellow card for a foul in the first half on Frédéric Guilbert, West Ham’s left-back invited punishment by grasping for Elmohamady’s jersey as Villa tried to launch a counterattack. When the Egyptian went down, Masuaku was sent off. “The typical second yellow card when you play away,” snorted Manuel Pellegrini, who claimed Villa were guilty several times of complaining about “fake fouls”. He made no mention of Mark Noble falling in the Villa box under no discernible contact.

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Pellegrini was pleased with how his team coped with going down to 10 men, agreeing with the midfielder Declan Rice’s opinion that West Ham would have lost in similar circumstances last season. “We have without doubt made progress in that sense,” he said. “We are working hard when we don’t have the ball and we are not conceding easy goals.”

Villa, bright for most of the game, became less dangerous when their opponents were supposed to be more vulnerable. They did not create a clear opening until two minutes from the end, when Douglas Luiz clipped a nice pass over to Jack Grealish, who bungled an attempted volley from 10 yards.

Grealish, eager to impress the watching Gareth Southgate, had a mixed game. He combined beautifully with Jota to produce Villa’s best chance of the first half, delivering a wonderful cross from the left. Wesley made a clever run to meet it but then headed over from five yards.

Facebook Twitter Pinterest Jack Grealish scuffs a volley into the ground in the final stages. Photograph: Martin Rickett/PA

West Ham mounted a counter-attack in the 20th minute, Andriy Yarmoleno providing oil in the form of a slick chested pass to Manuel Lanzini. Felipe Anderson crossed to Sébastien Haller, who got the jump on Tyrone Mings but nodded wide.

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Villa did most of the attacking, though, with Jota, Grealish, El Ghazi and John McGinn probing energetically on the platform given to them by Marvelous Nakamba who anchored midfield well on his debut before tiring and being replaced in the second half.

Wesley was canny and dynamic in the way he led the line but, like his teammates, short of sharpness at critical moments. Villa, who can take encouragement from many aspects of this performance, are set for more frustration if they do not find a way of penetrating. That means keeping their composure better than they did after Masuaku’s red card, when the whiff of victory made them almost dizzy.

“At 11 v 11 we were the better team and created the better chances,” said Smith. “The disappointing part is we never used our extra man well enough. We lost a little bit of emotional control and lost our structure. We had players giving sloppy passes away. We had players trying to do it all themselves, trying to take people on when you need to pass the ball a little quicker and draw people out. We didn’t do that in the last 20 minutes and that’s probably what were most disappointed about.”