The result left them with just two wins from their last 12 Premier League matches and entrenched in 14th place in the table.
The poor run has intensified pressure on head coach Thomas Frank, who is in his first season in charge following his move from Brentford.
Romero, the club's 27-year-old Argentine captain, apologised to supporters via social media after the defeat, with some fans seen arguing with players at full-time.
However, his message appeared to go beyond contrition, suggesting that Frank and the squad should receive stronger public backing from Tottenham's leadership.
The volatile centre-back initially posted a message that referenced "lies", a line widely interpreted as a swipe at the club's powerbrokers.
That post was later deleted and replaced with a near-identical version that removed the reference, though the underlying criticism of the board appeared to remain.
Tottenham's leadership structure has undergone significant change in recent months. Daniel Levy stepped down as chairman in September, with Vinai Venkatesham appointed chief executive in April.
Johan Lange has served as co-sporting director since 2023, while majority ownership remains with ENIC, the Lewis family trust, which is known for rarely making public statements.
"Apologies to all fans of you who follow us everywhere, who are always there and will continue to be," Romero said.
"We are responsible, there's no doubt about that. I am the first. 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. All together, it will be easier."
Tottenham captain Cristian Romero will sit out Saturday's FA Cup third-round tie against Aston Villa after being handed an additional one-match suspension by the Football Association.
Antoine Semenyo has completed a high-profile move to Manchester City and says he feels "so proud" to join the Premier League champions as he enters the prime of his career.
Antoine Semenyo has been spotted arriving in Manchester as he prepares to finalise his transfer from Bournemouth to Manchester City.
Thomas Frank has said Tottenham's latest setback was "extremely painful" after a dramatic stoppage-time defeat at Bournemouth, as the Spurs head coach faces fresh scrutiny following a chaotic night on and off the pitch.
