The Frenchman played a part in the only goal of the game, whipping over the corner that was eventually poked home by Bradley Wright-Phillips
With the Guners set to host and contest the Emirates Cup, the club's stopover 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 goalscorer in MLS - made the breakthrough in the 32nd minute for his seventh goal in six games for New York, who are 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 their Premier League opener at home to Crystal Palace on August 16.
Both teams were presented with sights on goal in an open start to proceedings in New York.
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 six yards out.
Arsenal were unfortunate not to be on level terms at half-time after midfielder Jack Wilshere was denied on by keeper Louis Robles and Tim Cahill in quick succession.
The visitors thought they had equalised 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 levelling goal but it was not forthcoming, as New York emerged triumphant on home soil.