Fulham exploited generous defending from their West London rivals to establish a 3-0 lead inside 41 minutes through the striker's double and a Clint Hill own goal.
Adel Taarabt pulled one back in the first half and Loic Remy added a second, moments after seeing a penalty saved, before Fulham lost Steve Sidwell to a red card for a late foul on Armand Traore.
And despite a late onslaught from the visitors, the Bulgarian always felt Martin Jol's side had enough quality to hang on.
"We have always been safe, I don't think anyone should worry - we play good football," Berbatov told Sky Sports 1.
"I was not nervous, we almost threw the game away, we had a comfortable lead.
"Maybe when they scored their second goal they believed. We held our lead we should score more, but three points is good for us."