Arsenal lost 1-0 thanks to Declan Rice’s strike at the start of the second half in another frustrating day for the Gunners.
Arsenal recorded 11 shots on goal but only got two on target as they lacked the finesse to make their mark.
And Koscielny thinks they were rushing things up top and needed to show more composure.
”I think in the final third we needed to keep more calm and not try to find the final ball and to continue to play with movement,” he said on Sky Sports.
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“In the second half we didn’t stop but conceded the goal early. We had some chances and we didn’t score. It is difficult to win if you don’t score. We need to keep our ambition and our game. We can come back.
“We needed to be clean with the ball and we weren’t. In football if you give a small chance to your opponent you pay and today we did.
“When you are arriving towards Christmas you know it is a big period and it is hard to compete at the same level.
“We started the new year with a win and we prepared for this game and came here with ambition for three points but we need to keep calm and focused on how we want to play.”
Arsenal could now be caught by Manchester United in fifth place if they beat Tottenham tomorrow.
West Ham have moved up to eighth in the table after Rice’s first goal for the club.
“I can’t put it into the words,” Rice said.
“The lads are always on at me to take the shot on more.
“I have been getting into the box more recently and I was gutted with missing the header in the first half.
“I can’t speak highly enough about Mark, he has helped me every day since I broke into the team three years ago with little pointers in training and whatever.”