Holland needed to beat Sweden by seven goals in the final qualifying game on Tuesday to secure a place in the play-off round but, despite a valiant effort, they could only record a 2-0 victory.
Bayern Munich forward Arjen Robben, who scored both goals against the Swedes, announced his retirement from international football after the match, ending a 14-year senior career with The Flying Dutchmen.
It is unclear whether Advocaat will stay on as manager but, if the 70-year-old does step down, he wants a thorough search for his successor to ensure they do not miss out on another major tournament.
"The KNVB must now find a good candidate for the future. I will be here until the friendly games in November. Although as Louis van Gaal said once 'never say never'," he told the NOS. "I have enjoyed my spell as national team manager for the 3rd time."
The Netherlands have now missed out on successive major tournaments, having failed to make the 2016 European Championship in France.