That victory at the Stadium of Light - Advocaat's first since assuming the reins from Gus Poyet - lifted Sunderland three points clear of the relegation zone.
However, the Wearsiders end their season with trips to Arsenal and Chelsea, so Advocaat is keen to do all he can in the meantime to secure his new club's position in the top flight.
"We cannot think any more of Newcastle, I have told them that," he said. "We have in principle five games in which we have to do it [survive].
"We still have a chance in the last two away games, but in principle, we have to do it in the first five games, so the most important game is now tomorrow."
Sunderland host Crystal Palace - managed by former Newcastle boss Alan Pardew - on Saturday.
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