Berbatov, whose agent this week indicated his client would look to move from Craven Cottage in January, was influential as Fulham's ended a six-game Barclays Premier League losing streak.
Berbatov laid on Fulham's first for Steve Sidwell before side-footing home a nonchalant penalty to make the points safe.
The result marked Rene Meulensteen's first win since replacing Martin Jol and built on the positive signs shown in the midweek loss to Tottenham, and Parker had nothing but praise for Berbatov's contribution.
"It was very good. We all know the quality he has," Parker told Sky Sports 1. "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."
Asked how key the result was, Parker said: "Massive. 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."
Fulham remain inside the bottom three but are only there on goal difference now after joining West Ham and Crystal Palace on 13 points.
And Sidwell, whose well-taken goal was his third of the season, is optimistic things are looking up under Meulensteen.
"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."