The Frenchman played a part in the only goal of the game, whipping in the corner that was eventually poked home by Bradley Wright-Phillips.
With the Gunners set to host and contest the Emirates Cup, the club's stop in the USA was brief and they left empty-handed after New York striker Bradley Wright-Phillips continued his impressive form at Red Bull Arena.
Wright-Phillips — the leading scorer in MLS — made the breakthrough in the 32nd minute for his seventh goal in six games for New York, which is fourth in the Eastern Conference standings.
Arsene Wenger, who is expected to announce the signing of goalkeeper David Ospina in the coming days, will oversee his team's upcoming fixtures against Benfica and Monaco ahead of its Premier League opener at home versus Crystal Palace on Aug. 16.
Both teams were presented with sights on goal in an open start to proceedings in New Jersey.
Arsenal icon Thierry Henry was the first to try his luck for the Red Bulls, flashing his shot just wide of the post in the eighth minute.
Aaron Ramsey attempted a similar effort 11 minutes later, with an identical result as the ball went wide after some good combination play from Arsenal outside the penalty area.
Henry was in and amongst it again in the 32nd minute as the Red Bulls broke the deadlock courtesy of Wright-Phillips.
The 36-year-old Frenchman delivered a corner that was headed across goal by Ibrahim Sekagya and Wright-Phillips pounced to poke the ball into the net from 6 yards out.
Arsenal was unfortunate not to be on level terms at halftime after midfielder Jack Wilshere was denied by keeper Louis Robles and Tim Cahill in quick succession.
The visitors thought they had equalized 10 minutes into the second half, when Abou Diaby raced through to place the ball beyond Robles, but he was flagged for offside.
The English club continued to press forward in search of a equalizing goal but it was not forthcoming, as New York emerged triumphant on home soil.