The Black Cats host Crystal Palace on Saturday looking to secure back-to-back league wins for the first time this season.
Victory over Newcastle in the Wear-Tyne derby lifted Sunderland three points clear of danger with seven games remaining.
But with the last week of the season seeing his side face a rearranged trip to Arsenal, before ending the campaign with a final day visit to Chelsea on May 24, Advocaat is anxious to have secured a ninth consecutive season in the top flight before the tough London double-header.
The 67-year-old refused to set a points safety total, but with four of their last six games away from home, he said: "We have those last two away games to end the season so ideally we have to do it (safety) in the next five games. The most important of those five games is tomorrow against Crystal Palace, because it is the next one.
"If we get a good result against Palace, the thinking might change as to how many points we need. We have to do it week by week and it's important to win the home games. It's better to do it game by game rather than look too far ahead."
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Dick Advocaat got his first win as Sunderland manager thanks to Defoe's stunning volley
Advocaat is desperate to avoid a post derby dip in form that could hinder his side's survival hopes, and the Dutchman added: "We have to forget about the win over Newcastle and concentrate on what will be a very difficult game against Crystal Palace."
The Sunderland head coach will decide between the fit-again Jack Rodwell and Adam Johnson as to who replaces Seb Larsson, the Swedish midfielder starting a two-game suspension after earning a 10th booking of the season against Newcastle.
Defender Wes Brown and midfielders Ricky Alvarez and Emanuele Giaccherini all remain out through injury.
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