"We have to respect Liverpool but of course do our job and trust ourselves, we did a great first half, almost perfect the way we controlled and blocked," Fulham coach Marco Silva said. "Second half we matched them every time.
"I know the quality Mitrovic has and I'm here to take the best from my players. Mitrovic is not just goals, he puts on the constant pressure and the overall job he did is fantastic."
Fulham grabbed their first goal on 32 minutes when they broke down the right hand side through Neeskens Kebano.
Nunez then scored to save Liverpool's blushes on his Premier League debut. He replaced Roberto Firmino on 51 minutes and scored just after the hour mark.
Salah levelled for Liverpool on 80 minutes after Nunez set him up.
"The best thing about the game was the result," Liverpool coach Jurgen Klopp said. "We got a point from a really bad game. The result was fine, I don't think we deserved more than that. The performance can be massively improved.
"We could have won the game because we had good chances but it was probably a bit too much today."