The Gunners have been title also-rans in recent years, with their last league triumph coming in 2004.
Chelsea are on course to lift their first title since 2010, as they are top of the table, seven points clear of the Gunners with a game in hand too.
And Wright thinks Arsenal can learn a thing or two from the Blues about grinding out results.
"We haven't seen that Arsenal for many years [the team who beat Manchester City]," Wright told BT Sport.
"You can see us in there, but they need to get it to come out consistently.
"Go somewhere like Burnley and win 1-0, go to City and beat them 2-1 and knick something at someone like Burnley.
"They have got to learn like Chelsea do - do not lose, win ugly."