Arsene Wenger lamented his team’s weakness in the air after seeing Andy Carroll score a hat trick in the 3-3 draw at West Ham on Saturday that badly damaged the Gunners’ slim title hopes.

Arsenal were 2-0 up in the first half, only for Carroll to level with two quick goals just before half-time — the first with a header and the second after controlling a cross and scoring with his boot. He then put West Ham ahead with another powerful header from a pinpoint cross early in the second half before Laurent Koscielny equalised.

“We paid for our weakness in the air inside the box. And since the beginning of the season in some important games that has happened to us,” Wenger told BT Sport. “It’s disappointing for us, especially with players of that experience, 2-0 up on 43 minutes and at 45 it’s 2-2. I think that’s where we have made it difficult for ourselves.”

The draw diminishes Arsenal’s already small chances of catching leaders Leicester, who can go 13 points clear of the Gunners with a win at Sunderland on Sunday. But Wenger refused to say his team’s title challenge is over.

“Over, no. But it makes it much more difficult of course,” he said. “We have to wait for the [other] results and focus on the next game. Because they are chasing behind us as well and we dropped two points today.”

Wenger opted to start an unchanged side from his team’s 4-0 win over Watford, which meant David Ospina remained in goal with fit-again Petr Cech on the bench. Ospina had deputised for Cech while he recovered with a calf injury and kept a clean sheet against Everton and Watford, and Wenger defended his decision to stick with the Colombia international.

“Look, does Petr Cech play or David Ospina? We have a bad record in the air since the start of the season no matter who plays,” he said.

“We have not conceded in the last two games. And if you look at the numbers of both keepers, no matter who you play you are right, and no matter who you play you are wrong. Because every time you concede a goal people will say, why didn’t you play him or him? … I just decided to keep the winning team.”

Wenger also said Carroll was lucky to stay on the pitch after two incidents where he first hacked down Koscielny from behind and also threw an elbow at Gabriel Paulista during an aerial duel.

“There were one or two controversial situations in the game where I think he could have been sent off. But overall, that doesn’t mean we have to concede the goals after,” Wenger added.

However, West Ham manager Slaven Bilic said it was unfair to blame the Arsenal defenders for not being able to handle Carroll.

“To some point you can say that, but Andy Carroll is doing that kind of thing against any centre-backs,” he said. “He’s done it against Liverpool, against Chelsea and against Arsenal… We had great deliveries today, more than three times, and it’s perfect for him.”