Chelsea reached the last 16 of the Champions League with a 3-0 victory at home to Valencia on Tuesday but have fallen off the pace domestically and are in fourth place, 10 points behind unbeaten City.
"For us, its either we continue to challenge for the Premier League if we win or if we draw, [but] our Premiership becomes extremely difficult if we lose," Villas-Boas told reporters.
"There is no quitting and there will be no quit belief. But 13 points will be a massive gap."
City have been rampant so far this season, dropping just four points in 14 league matches and scoring 48 goals, although they did suffer a setback on Wednesday when, despite a 2-0 home win against Bayern Munich, they were eliminated from the Champions League.
Villas-Boas praised Roberto Mancini's outfit and warned that with every passing victory they will toughen mentally, making them even harder to overhaul from the top of the table.
"It's difficult to find weaknesses in a top quality side like Manchester City at the moment," he said. "They are more than fair leaders with outstanding performance levels."
"Motivation has been top for them and in the end motivation is decisive. I think the further they go on in the league with the amount of wins that they have been having, the further that they believe this can be their year. This has a major impact."
Last week Chelsea won 3-0 at high-flying Newcastle United and Villas-Boas, whose own position has come under scrutiny in recent weeks, said his side's recent improvement was largely down to stronger defensive displays.
"The Newcastle win was a good response. In the Premiership we are showing good signs of recovery from a bad period between [losses to] QPR and Arsenal. Out of four games, we have three wins and three clean sheets.
"It does mean that our defence is competent and our defensive organisation is solid."
France striker Nicolas Anelka and Brazilian defender Alex have stopped training with the Chelsea first team after handing in transfer requests and there has been speculation that midfield stalwart Frank Lampard could be set to leave the club as Villas-Boas aims to reduce the age of his squad.
Lampard, who has been linked with the MLS in the U.S., was an unused substitute for the crucial match against Valencia in midweek but Villas-Boas brushed away speculation about the future of Chelsea's old guard.
"We have a lot of competence in the team. Everybody is challenging for their place. The conversation for Lamps is exactly the same for all of the players," Villas-Boas said.
"All of them are competing to be the best, to be in the starting XI. All of them deserve credit and he'll turn things around for sure."
