The Bulgarian striker assisted Steve Sidwell for the opening goal, before nonchalantly doubling the lead with a penalty nine minutes later, despite talk of him wanting an exit during the week.
Berbatov's agent had claimed that the 32-year-old would be looking for a January move, but he showed no signs of that and Parker hailed his display as the Cottagers claimed their first win in seven games.
"It was very good. We all know the quality he has," he told Sky Sports.
"He was exceptional again today and was on Wednesday.
"We all need to put in a shift and he's part of the team and we need to carry on from where we've left off today. We all knew how important today was, we put in a shift and got the three points.
"We needed to pick up some points. We had a good performance on Wednesday and followed up with a win."
The result marked Rene Meulensteen's first win in charge of Fulham, and goalscorer Sidwell thinks that the former Manchester United assistant has already made an impact at Craven Cottage.
"We've tried different formations since he's took charge," he said.
"There's versatility in the squad, we all put in a shift and hopefully it's working now."