The Toffees remain just one place above the drop zone and four points clear of Burnley ahead of their trip to Turf Moor.
Rooney said on Sky Sports' Monday Night Football. "I got approached by Everton to do an interview for the manager's job - as I've said before - and I'm at Derby.
"I'm still learning and I felt it wasn't the right time. Frank has gone in there and it's a tough job where they've been all season.
"I didn't feel Rafa (Benitez) was the right fit for Everton coming in. That didn't work out and the players have lost confidence.
"Since Frank has come in, he's tried to create a mentality in the players but the damage has already been done in the early part of the season.
"It's how they crawl themselves out of that. They've got a massive game on Wednesday away to Burnley and I feel it's a must win.
"I'm very worried [as a supporter]. It was a better performance against West Ham but once you're in that run of form and you find things difficult - you look at the second goal where (Alex) Iwobi gives the ball away - and these things seem to always happen.
"They just need to hang in there and find a way to pick up results, like they did against Newcastle. That was a game where Newcastle were the better team on the night but Everton won that through fight and being horrible to play against.
"I don't want to question the Everton players' will to fight because I don't know what their characters are but that Newcastle game showed they can do it - especially at Goodison. They have to go and fight for the shirt and for the club.
"The Burnley game is huge because they've got tough fixtures. They can get results against those teams but the Burnley one, for confidence, for belief and for the fans... it's a must-win game. They have to go in and leave everything out on the pitch."
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