Villas-Boas, however, insisted that neither his job nor Chelsea's season hinged on the outcome of the club's Champions League clash with Napoli.
Villas-Boas' players did nothing to ease the pressure on their manager with a performance on Saturday that almost saw them dumped out of another competition.
Chelsea will need to improve immeasurably to avoid crashing out of the Champions League, with only two days to find a solution to their miserable form before the first leg of their last-16 tie in Italy.
But even if they fail to progress, Villas-Boas was confident he would not be sacked by billionaire Blues owner Roman Abramovich.
Asked if the outcome would have any impact on his future, the 34-year-old said: "No, not at all.
"It's not up to me to decide that. You have to ask that question to the right person."
Chelsea's performance on Saturday appeared to show Sunday's summit meeting between Villas-Boas and his players had little effect.
The Blues boss was reportedly challenged openly by some of his squad during frank exchanges, but if he was expecting a positive response, he failed to get it as they stuttered to a 1-1 draw against below-strength npower Championship opponents.
"We were not good enough," Villas-Boas said.
"Better in the second half but not enough to win the game.
"Never satisfying when you draw at home to a Championship team."
The latest in a long line of defensive mistakes this season saw Birmingham take the lead through David Murphy.
Daniel Sturridge eventually equalised but Chelsea simply did not do enough to merit a winner.
Villas-Boas, who hauled his players in on their day off on Sunday after a display at Everton he branded the "worst of the season", denied they had been as poor today.
"The team commitment was there and the team response was there straight after we suffered the setback," he said, pointing out they immediately won a penalty missed by Juan Mata.
"If the penalty goes in, it's 1-1 a little bit earlier and it gives you time to find the winner.
"It took us too much time to score the leveller."
Part of the reason for that was another abject performance from Fernando Torres, who was unsurprisingly replaced by Didier Drogba at half-time.
Torres did not sit with his team-mates on the bench for the second half, which Villas-Boas said the Spaniard watched from the dressing room.
He added: "I'm sure that he didn't take it lightly but it's a decision for the benefit of the team."
Villas-Boas branded suggestions Drogba had delivered a half-time team-talk before his introduction as "ridiculous" but admitted captain John Terry - who did not play today - may have complained to the referee about time-wasting.
Villas-Boas revealed Terry was only "50-50" to return from a knee injury against Napoli after failing to train on Friday but was more optimistic about Ashley Cole shaking off a calf problem.
Birmingham boss Chris Hughton hailed his own side's display as their best of the season, especially considering they were without Nikola Zigic and Marlon King, and lost captain Stephen Carr early in the game.
"I'm more delighted not so much with the result as the performance," Hughton said, admitting his side took advantage of Chelsea's recent poor run.
He added: "A Premier League team playing against a Championship team at home are always going to be favourites.
"Any unrest, it's normal, but I'm quite sure that they'll go on to have success because of the quality of player that they've got."
Hughton said of the pressure on Villas-Boas: "It very much comes with the territory.
"He is an exceptional manager. You don't get the type of job that he's got without being that.
"I think he's gone through a transitional period, perhaps with the way that they're playing and the players than they have.
"Sometimes it takes that little bit longer."
Hughton revealed full-back Carr's latest knee injury would be assessed ahead of Tuesday's trip to Barnsley.
He added: "The big blow for us is that he's only just come back from a lay-off."
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