A 78th-minute penalty from Evandro saw Estoril to an upset 1-0 win at the Estadio do Dragao, where Porto had been unbeaten in the Primeira Liga since October 2008.
The end of the 81-match unbeaten league run at home saw Porto stay third, four points behind leaders Benfica, who have a game in hand.
In a television interview after the game, Fonseca, whose team were jeered off, said he would speak to the president about his future.
But in his post-match news conference, Fonseca said his side would continue fighting despite their first home league loss since October 2008.
"If this game had gone as usual, FC Porto would have won," he said.
"There were no issues with the commitment or effort shown by the players, but what will be remembered is the final score.
"Truth is we lost, which made everything harder, but we are not throwing the towel."
Benfica face Vitoria Guimaraes on Monday and could move seven points clear of Porto and five ahead of second-placed Sporting Lisbon with a win.
