Arsene Wenger's side, who were defeated by North London rivals Tottenham Hotspur last time out, slipped eight points outside the Champions League qualification places with the loss, which was followed by victories for Liverpool and Chelsea.
Wright also wrote in his column for The Sun that Wenger's team could struggle to compete in the later knockout rounds of the Europa League.
"Fourth spot in the Premier League now looks impossible for Wenger. Saturday's 1-0 loss to Spurs pretty much ended any hopes," the 54-year-old wrote. "To close a gap with an inferior goal difference — and just 11 games left to play — would be an incredible achievement.
"For Arsenal to win the [Europa League] final in Lyon on May 16 could still be one hell of a task when you look at the teams competing. But if this team can struggle at Swansea [City], you have to wonder what would happen if they took on Napoli, [Borussia] Dortmund, [AC] Milan or Atletico Madrid in Europe.
"The team must not give up and really fight hard in Europe as stranger things have happened. But most fans will not be holding their breath."
Arsenal play Ostersunds in the last-32 of the Europa League on Thursday.