Jagielka has been on the sidelines since October due to a medial knee ligament damage.
The 33-year-old central defender is close to making a comeback, with Everton manager Roberto Martinez quoted as saying by The Guardian that he could feature against Tottenham Hotspur, Manchester City or Dagenham & Redbridge.
"I don't necessarily think it is a case of needing new personnel - it's just the way they play,” Sutton has told BBC Sport. “They are expansive, bomb the full-backs forward, it leaves holes at the back and they are caught out because of their style of play.
“Phil Jagielka is coming back from injury - but it would be the same with him playing."
Jagielka, who has been on the books of Everton since 2007, featured in 10 Premier League games this season before getting injured.
The England international centre-back created one chance, had a pass accuracy of 82%, and won 25 headers, one dribble and six tackles in those 10 league matches.
Everton are 11th in the Premier League table at the moment with 26 points from 19 matches. Martinez’s side will return to league action on Sunday afternoon when they take on Tottenham Hotspur at Goodison Park.