Berbatov scored the only goal of the game in the first half with a stunning volley to ease the Cottagers' relegation fears.
However, Fulham were indebted to goalkeeper Schwarzer's second-half penalty save from Jon Walters to secure all three points.
The win moves Fulham onto 32 points and Berbatov hopes Martin Jol's side can build on the win to continue to climb away from trouble at the wrong end of the table.
"Today was important but it's not going to mean much if we lose the next game," Berbatov told Sky Sports HD2.
"Today we played very good football. We know Stoke play the long ball and have strong players but we managed it very well and got the three points, which is most important."
Berbatov's goal was the one outstanding moment in the game and the Bulgarian admitted he practises on his volleys in training.
"It's all about the practice," added Berbatov.
"I practise in training and score against (Fulham goalkeeper) Mark (Schwarzer) all the time. You just need to do something special and you do it.
"It is a good one, but I have better ones."
Schwarzer was not surprised by Berbatov's stunning effort saying: "We see it every day in training.
"We know what quality he has and expect it from him, which puts more pressure on him."
Schwarzer also revealed that he did his homework on Walters' penalties and was confident of saving his effort after Ashkan Dejagah handled inside the box.
"We looked at video footage before the game so I was confident I knew where he was going to go. I was lucky enough to get behind it," added Schwarzer.
Schwarzer also made a good save to deny Peter Crouch early in the second half and he was delighted to keep a clean sheet.
"Any time you don't concede a goal is important," noted Schwarzer.
"We needed the points today. You know what you are going to get from Stoke and it is especially vital at home to pick up three points."