Sunderland led 2-0 and looked as if they were heading for their first league win of the season before having goalscorer Jermain Lens sent off in the second half and allowing the Hammers to leave the Stadium of Light with a point after a 2-2 draw.
Asked at the post-match news conference if he had decided on his future, the former Netherlands manager replied "yes" but declined to say what that decision was.
Earlier he told the BBC: "I don't want to give an answer. Today I am the manager, what will happen in the next weeks, months, I cannot say.
Asked if he would be manager for the next game, he added: "I cannot say that. The newspapers have to have something to write otherwise there is nothing in the newspapers."
Earlier he told Sky Sports he was delighted with the way Sunderland played at the start of the match when Steven Fletcher and Lens scored to put them in control.
But Carl Jenkinson halved their lead just before the break and Lens saw red in the second half when Dimitri Payet salvaged a point for the visitors.
"The way we played in the the first half was the best I have ever seen from the team, it was a difficult moment when Lens got sent off, but I am very pleased with the way they worked," said Advocaat.
The 68-year-old Dutchman replaced Uruguayan Gus Poyet as coach in March when Sunderland looked doomed to relegation but he kept them in the Premier League after they lost only two of their last eight matches.
He made no secret he intended to retire in the summer but changed his mind and continued in the dugout this season.
But for the third season running, Sunderland failed to win any of their opening six league matches and Saturday's draw has stretched that run to eight games since the season started.
The one bright spark for long-suffering Sunderland fans is that the point at least lifted the club off the bottom of the table, replaced by arch-rivals Newcastle United who lost 6-1 at Manchester City.
(Reporting by Mike Collett, editing by Alan Baldwin)
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