The Cherries triumphed 3-2 at Dean Court last night, with Antoine Semenyo scoring a 95th minute winner.
In the aftermath, Romero posted to Instagram, insisting "other people" should be speaking with Spurs now sitting 14th on the Premier League table. The Argentine's comments being viewed as a shot at the board.
"Apologies to all fans of you who follow us everywhere, who are always there and will continue to be," Romero posted.
"We are responsible, there's no doubt about that. But we will keep facing up to it and trying to turn the situation around, for ourselves and for the club.
"At times like this, it should be other people coming out to speak, but they don't - as has been happening for several years now. They only show up when things are going well.
"We'll stay here, working, sticking together and giving our all to turn things around. Especially at times like this, keeping quiet, working harder and moving forward all together, is part of football."