The Toffees remain in a Premier League relegation dogfight despite a change in the hot seat in January.
Rafa Benitez was axed just six-and-a-half months into the job following a horrendous run of one league win in 13 matches.
But his successor Lampard has managed to deliver only two top-flight victory in eight games - and lost the other six.
As a result, Everton are left sitting 17th in the table. They’re just three points above the drop zone ahead of a huge trip to 19th-placed Burnley tomorrow.
Rooney, who turned down a chance to be interviewed for the Goodison Park job to remain at crisis club Derby County, reckons the Blues players' confidence jettisoned under Benitez - and it's becoming difficult to get that back.
Speaking on Sky Sports' Monday Night Football, the ex-Everton forward said: “I got approached by Everton to have an interview for the manager’s job.
“As I’ve said, I’m in a job, I’m at Derby, I’m still learning and just felt it wasn’t the right time.
“Obviously, 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 person coming in.
“That didn’t work out, the players have lost confidence and since Frank come in, he’s trying to create a mentality in the players.
“But I think a lot of damage has already been done in the early part of the season.
“It’s how they claw themselves out of that.
“They’ve got a massive game on Wednesday against Burnley away. I think it’s a must-win.”
‘Fight for the shirt’
Everton suffered a 2-1 loss at West Ham United on Sunday.
But in their previous league game before the international break, the 10-man Toffees clinched a crucial 1-0 win over Newcastle.
Rooney believes the fight Lampard's troops displayed against the Magpies needs to be replicated in the remaining 10 games to avoid relegation.
He added: “The West Ham game was a better performance, but once you’re in that run of form, you find it difficult.
“For the second goal, [Alex] Iwobi gave the ball away and these things always seem to happen.
“They just need to hang in there and find a way to pick up results - as they did against Newcastle.
“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 we don’t know what their characters are.
“The Newcastle game showed they can do it. Especially at Goodison, you have to fight for the shirt and the club.”