Tuesday's 2-0 League Cup quarter-final defeat by Liverpool came hot on the heels of a Premier League loss to the same club and a 5-3 defeat by Arsenal to make fans twitchy at a ground that had been a fortress for much of the Roman Abramovich era.
"For our Premier League challenge to be alive we need to make the most of the December fixtures," the manager said on the club website.
"We play most of the top teams and that is our challenge for December. March and April can be as decisive, but as we play the top teams it's a fact."
"The Champions League is a life and death situation and we will need to up the tempo and play with desire," Portuguese Villas-Boas said.
Villas-Boas can feel the tension in the air after overseeing the club's worst start to a season since the Russian's arrival.
"You can feel Stamford Bridge has become anxious when we play at home but we need their full support, it's the only way you can build the right atmosphere," he said.
"We have two big games at home now [Valencia and City] where we need the fans right behind us.
"Away from home we've been more solid, statistically and as a team. At the moment, when we play at home we've not been good enough, we need to get our fans behind us."
Villas-Boas has said he has Abramovich's backing despite the poor run, making media reports that his job is under threat seem premature, but if he does not turn things round in December then that speculation over his future will only grow.
