The 68-year-old blamed a lack of spending power for the north east team's slide to second from bottom in the English Premier League.
"If you are at a club like Sunderland, a club that has less money to spend than many of the others, what has happened now is inevitable... and I have no appetite for that," Advocaat told the Dutch TV channel NOS on Monday.
"I’ve never had the habit to just stop but after eight games with just three points I had the feeling I’m not the right man to be leading the team. I’ve never been in this situation before and I didn’t really see any other solution.
"I have not asked for any settlement money nor received any and I’m 100 percent sure I’ll never coach a club again. But it would be nice to help a country to qualify for the Euros, I would really like to coach at a Euros."
Advocaat, who took over from Uruguayan Gus Poyet in March, had initially planned to leave Sunderland at the end of last season but stayed on after they staged an escape act to avoid relegation.
"I have no regrets about extending my contract, absolutely not," said the Dutchman.
"I always wanted to work in the Premier League. I had worked in Scotland but England has a much superior league," added the former Rangers manager.
The much-travelled Advocaat previously coached Netherlands, United Arab Emirates, South Korea, Belgium, Russia and Serbia.
At club level he has also been in charge of Borussia Moenchengladbach, Zenit St Petersburg, AZ Alkmaar and PSV Eindhoven.
(Reporting by Mark Gleeson; Editing by Tony Jimenez)
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