Barrett boasts a 1-1 record since being installed as interim coach following the axing of Brad Arthur last month.
Boosted by the return of Mitch Moses, the Eels enjoyed a 34-22 win over Cronulla in their last outing.
The victory over the Sharks shapes as a potential springboard for the Eels' season with winnable fixtures against Canterbury on Monday, the Sydney Roosters, Newcastle and South Sydney over the next four weeks.
A successful run could help Barrett's audition for the full-time role after the former Manly and Bulldogs coach threw his hat in the ring for the role in an interview on Sydney radio station 2GB on Saturday.
"It's a really good club to coach as well and we've got good players, so that certainly makes my job a hell of a lot easier," Barrett said on Sunday.
"We've got a good mix of players, some senior blokes in there who know what they're doing and they just need a bit of guidance.
"But we've got to back up what we did last week.
"It can't be about me, it's definitely not and that sort of stuff will look after itself.
"We (the club and I) know where we both stand and we've had a few conversations but as I said, I don't want that to be a distraction and I certainly won't let it."
Mitch Moses was left bloodied but led the Eels to victory over Cronulla on his return. (Dan Himbrechts/AAP PHOTOS)
Moses's fitness helped spark Parramatta against the Sharks and an impressive performance could lead to the halfback returning to the NSW State of Origin side.
The Eels have won four straight over Canterbury and Barrett wants to see the No.7 continue his faultless run of form.
"He gives everyone else around him enormous confidence as most halfbacks do," Barrett said.
"He's at a good age now, Mitch, where I think he's pretty comfortable with what he needs to do on the field and off the field.
"In the position that he's in he has played a lot of footy now and he's playing very well."
