The Blues have fallen off the pace somewhat domestically despite qualifying for the last-16 of the Champions League – a feat both City and Manchester United failed to achieve this season.
If the west London side lose against the table-toppers at Stamford Bridge they will fall 13 points behind the league leaders, and Villas-Boas acknowledges this will be a tough deficit to overcome.
He told reporters on Friday: “We continue to challenge for the Premier League if we win or if we draw.
“But the Premiership becomes extremely difficult if we lose – because 13 points away would be something [worse] than what is already a big, big distance.
“There will be no quitting. It's not impossible to recover, but that's a reality.
“We all agree at the moment that Tottenham and Man United are the teams up there challenging.”
Chelsea have won three of their last four matches 3-0, but their manager is aware that Roberto Mancini's side will be favourites coming into the tie due to their recent form, remaining unbeaten still in the league.
Villas-Boas continued: “They are going to put on a massive, massive challenge for us.
“When you see a leader of this dimension, there's not a good time to play them. They are outstanding, week in, week out.
“I'm sure they will play to gain the three points – they will come out almost with the assurance that their Premiership title is at least with one team less in the running.
“I think it's fair for us to see how it is after all the December fixtures, but the further they go on in the lead with the amount of wins they have been having, the further they believe that this can be their year.”
Despite dominating the Premier League, the two Manchester clubs will play Europa League football for the remainder of the season, however Villas-Boas rejected the notion that it improves his own side's chances in the Champions League.
“I really don't know if the Manchester clubs playing in the Europa League gives us an advantage,” the former Porto coach continued.
“I don't think it changes a lot. But a win would mean a return to consistency in terms of results. We could finally say that we got our run back.”