Eddie Howe was torn between elation and relief after one of the games of the season, but the crucial penalty decision against Kalvin Phillips as West Ham lost 4-3 at Newcastle from 3-1 up left David Moyes lamenting what he called “a poor run” of decisions from referees.

Harvey Barnes was the match winner with two late goals. “It was one of the maddest games I’ve played in,” he said after reviving Newcastle’s hopes of securing European qualification.

“It’s one of those days you are going to remember for a long time. We’re all about team spirit and we showed an abundance of it. We never give up.”

Related: Harvey Barnes’ late double sees Newcastle sink West Ham in thriller

Howe said: “It was a brilliant advert for the Premier League. At 3-1 down it looked a really difficult point in our season but the players remained calm. They’re incredible professionals and that’s an incredible win for us.”

Barnes has spent much of the season sidelined by a foot injury after his £38m move from Leicester last summer but the winger was finally able to prove his worth. “Harvey’s a goalscorer,” said Howe. “He’s been struck by injuries and had a really difficult start to his Newcastle career but the quality is undoubtedly there and he scored two brilliant goals.

“It gives us renewed confidence – and hope. We still feel we have an opportunity to make something of our season. If we’d lost it would have been difficult to do that but, when you’re chasing a game you want chaos and we definitely had that.”

Moyes was rather more downbeat. “I’m gutted. This feels like a bad defeat,” said West Ham’s manager. “We did a lot of good things and were a threat but we didn’t defend well enough. I don’t think you can say we were in control at 3-1.”

He did not enjoy watching Anthony Gordon win two penalties converted by Alexander Isak and was particularly exercised by the second, when the England winger was caught by the substitute Phillips. “Gordon restricted Kalvin Phillips from kicking the ball,” said Moyes. “It was the wrong decision. The player actually places his leg to be kicked.

“We’ve had an incredibly poor run of stuff from referees. It was a day when very few decisions went for us.

“Anthony Gordon had planted his leg because obviously Kalvin Phillips is looking forward. He’s just about to clear the ball. He [Gordon] plants his leg in front of it and he [Phillips] kicks the back of his leg. You need to decide what way you want to look at it.

“It’s small margins. We’ve lost a game we should have won. This is a tough place to come and we didn’t see the job through. Newcastle have some very good attacking players and we weren’t tough enough. We have to be harder to play against.”