Spurs looked set to salvage a point when captain Romero headed home Pedro Porro's cross in the 64th minute, lifting the crowd after a poor first half. But Tottenham were punished deep into stoppage time as Callum Wilson scored a late winner, prompting angry chants from supporters aimed at Frank.
The loss was Tottenham's third in a row and their eighth in 14 Premier League matches, leaving them 14th in the table and out of both domestic cup competitions. The atmosphere at full-time was toxic, with boos echoing around the stadium.
Speaking afterwards, Romero thanked the fans for their support but urged calm. "It's difficult and it's a disaster moment for us," he said. "Now we need silence, work hard every day and stay together. In three days we have another big match."
That focus turns to the Champions League, where Spurs still have a chance of finishing in the top eight. They sit just above Borussia Dortmund on 11 points and host the German side on Tuesday before travelling to Eintracht Frankfurt later this month.
Frank, whose future is under scrutiny despite backing from the club hierarchy, accepted responsibility for the results but insisted progress is being made. He pointed to the effort of his players, while admitting a lack of cutting edge in attack.
Tottenham's problems are compounded by absences, with Conor Gallagher ineligible in Europe, Micky van de Ven suspended and several players carrying injuries. As Romero stressed, unity and hard work are now crucial if Spurs are to rescue their season.
Liverpool head coach Arne Slot said he fully understood the frustration of supporters after his side were held to a 1-1 draw by Burnley at Anfield, admitting the reaction at full-time was justified.
Mikel Arteta was left frustrated after Arsenal's title charge lost momentum in a goalless draw against Nottingham Forest, insisting his side were wrongly denied a decisive penalty late in the contest.
Crystal Palace are preparing for life after Oliver Glasner, with the Austrian confirming he will step down as manager when his contract expires at the end of the season, bringing an end to a transformative but turbulent era at Selhurst Park.
AS Roma have strengthened their attack with the signing of Netherlands international Donyell Malen from Aston Villa.
