Striker Diafra Sakho made his first appearance since November after recovering from a back injury, although he only touched the ball eight times after his second-half introduction.
Michail Antonio is to be offered a pay rise as a reward for his outstanding performances this season, West Ham manager Slaven Bilic said on Tuesday.
Coming off an impressive season a year ago, where the Hammers finished 7th in the league, with a very in-form Dimitri Payet at their disposal, things haven't exactly gone the same for this campaign.
The loss was West Ham's fifth in succession, while they are now seven winless since a 3-1 victory at Southampton over two months ago.
The Arsenal manager has, perhaps, regained the trust of large portions of Arsenal fans with recent results - a spirited draw with Manchester City at the weekend doing little for their top four chances but at least displaying a modicum of bottle which has so often been absent this season. Sometimes you don't want to see it, even when you want to just text with friends or look at pictures that your family posted or whatever. What we want is to come back to win our games.
With Koscielny injured, Theo Walcott could be set to captain the side in the midweek clash against West Ham at the Emirates as he is the most senior player available. I tell myself to finish as high as possible.
Think you can do better than Lawro?
Roger Federer Wins Miami Open, Sports New Rolex Sky-Dweller
In a close opening set, the old adversaries shared 10 break points with Federer securing the crucial break in the eighth game. Federer has beaten Nadal in all of those events this year and has now won his last four meetings between the pair.
Arsene Wenger and his side came into the game under increasing pressure, with Arsenal having won just one of its previous six league games.
With midfielder Andrew Surman suffering a knee injury at Southampton, Wilshere, Harry Arter and Jordon Ibe are in contention to replace the South African in the starting lineup for the league match at Liverpool on Wednesday.
Arsenal are now sixth and seven points off fourth-placed Manchester City, although with a game in hand. It has been 13 years since they last won the league.
Arsenal have scored 14 headed goals in this season's Premier League, a figure matched only by West Brom.
Alexis Sanchez has scored four goals and provided one assist in his last two games against West Ham, including a hat-trick in the reverse of this fixture.
Will West Ham ever win again?
The Croatian will do battle with his French counterpart this evening at the Emirates with both clubs struggling for form in the Premier League.