The Toffees' woes away from home continued as they crashed out of the FA Cup at Crystal Palace yesterday.
The Blues' primary focus this season is ensuring they do not suffer relegation, though.
Lampard's side currently sit three points above the drop zone with 11 matches remaining after beating Newcastle United last Thursday.
What’s been said
Cole, speaking on ITV after Everton's loss to Palace, believes Lampard wouldn't have realised the size of the task he took on until after walking through the Goodison Park door.
But the ex-Chelsea winger believes his former team-mate will ensure Everton retain their top-flight status.
Cole said: “It's certainly a very difficult time for everyone at the football club.
“Frank has come into the club - and I don't think walking in through the door, he'd have realised how difficult it is going to be.
“There are five or six players there who are really low on confidence. When you're in a relegation battle, the fundamentals they were getting wrong, the decision-making on the pitch.
“I know Frank and I know his team. He'll be drilling them and drilling them.
“This has been a distraction in a way because they had that massive win on Thursday night that lifted the whole place and you probably want to roll into another Premier League game and get some momentum.
“But he has tweaked his team around, another disappointment is the injury to [Andros]Townsend, that's the last thing you need today.
“But I have no doubt he will steer them out of it and they'll be fine.”