The Cottagers suffered a 4-1 away defeat to Manchester United in the fourth round of the competition on Saturday.
"It's no guarantee of safety, but on the other hand, I always like it if teams, especially those around us, have replays or stay in the Cup," The Mirror quotes him as saying.
"So in that respect it's probably better to be out of it. It's quite simple – we need four or five wins. But if you leave it up until the end of the season, you could probably end up with a problem.
"If we win those games as soon as possible, it could be easier. I think you will need 36 or 37 points to be safe and at present, there are probably eight teams who are fairly concerned."
Fulham are currently six points above the relegation zone in 14th place.