A Phil Jagielka first-half strike was enough for Everton to claim all three points at stake in the Premier League tie.
Arsenal are preparing for their quarter-final first leg Europa League clash with Napoli and did not start influential stars, Aaron Ramsey and Pierre-Emerick Aubameyang against the hosts.
And Wright has said the Gunners boss made a mistake by taking the decision, blaming it for the team’s defeat by the Toffees.
“I was a little bit disappointed with Arsenal’s selection,” Wright said. “They’re in fourth position, no-one would have thought at the start of the season that it would have happened like it has.
“So it was an opportunity to start Aubameyang, start Lacazette, get Ozil on the pitch, start with Ramsey – get your best players on the pitch and really have a go at Everton.
“I thought we missed a trick in that respect. In the end, Everton had the impetus…I think it was fortunate that they didn’t get another goal.”