The Gunners were beaten 1-0 by the Foxes at the Emirates after Jamie Vardy scored late in the second half.
Mikel Arteta’s side controlled the game in the first half but they struggled to find an opener and Leicester slowly came into the match, particularly once Vardy was introduced from the bench.
The Spaniard was critical of his side’s failure to make their domination pay in the opening 45 minutes and Wright feels United’s speedy frontline could make Arsenal pay if they don’t find a way of ‘digging in’.
‘You look at Manchester United as well who are another team that will want to play on the break,’ said Wright, after Arsenal’s defeat.
‘You’re going to need to be able to pass through them, be able to break them down. Manchester United will do the same thing [as Leicester] and they’ve got even better players going forward, more than just Vardy.
‘It’s a tough one, we knew Leicester were going to be tough and we know Manchester United are going to be tough.
‘Arsenal are going to have to dig in and find a way of getting results without scoring the perfect goal.’
Later on in the show, Wright added to his comments on Premier League Productions: ‘With the counter-attacking, you look at Arsenal and you can see what happened with Vardy there tonight. Rashford could cause us problems.
Arsenal’s defeat means they have just nine points from their opening six matches, while United have similarly struggled by amassing just seven points from their five matches.
The Gunners fear they could be without David Luiz for the trip to Old Trafford after the Brazilian was forced off in the second half against Leicester with a suspected thigh strain.