The club captain, 33, returned to the team but could not lead his side to a first away Premier League win since the end of November.
In truth, the Gunners never looked likely to score and struggled to threaten at the London Stadium.
And Koscielny was not afraid to make his feelings clear in his TV interview.
He said: ”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.
"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."
Unai Emery opted for the 3-4-3 formation with a front three of Pierre-Emerick Aubameyang and Alex Iwobi either side of Alexandre Lacazette.
Lacazette started well and went close with a volley on the turn while midfielder Matteo Guendouzi's powerful strike from the edge of the area flew just past the top corner.
Emery is turning Arsenal into a mediocre side while superstars Ozil and Torreira are being wasted
SURPRISE, surprise there was no Mesut Ozil or Lucas Torreira for Arsenal and surprise, surprise there was once again no cutting edge at the London Stadium.
It was another case of a lethargic opening 45 minutes and things did not get much better after half-time.
Declan Rice’s first West Ham goal – just two days before his 20th birthday – settled this lacklustre game with a neat finish.
Felipe Anderson did well but Arsenal failed to get rid and the young midfielder punished them.
And there was no way back as Arsenal look set to fall further behind the top four later on this weekend.
Their fans have had to get used to slow starts under Unai Emery – who is not doing himself any favours with his team selections, it has to be said.
He has an excellent, talented squad at his disposal, no matter what anyone might say, but he is simply wasting it by leaving some of his best players out.
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Arsenal managed 11 shots in the game with just two hitting the target and threatening former Gunners stopper Lukasz Fabianski's goal.
And their poor display in front of goal came back to haunt the Gunners when Declan Rice punished them.
He showed the calmness Lacazette & Co didn't when he side-footed his effort into the top corner to score the only goal of the game.
This defeat extends a rot away from the Emirates for Emery's side: the draw at Brighton on Boxing Day was sandwiched between defeats at Southampton and Liverpool and Arsenal could end the day six points off the top four with Chelsea in North London next weekend.
Koscielny added: "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.”
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