The draw left Liverpool needing a maximum of four points from their remaining two matches to guarantee qualification for the Champions League via a top four finish.
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They will host third placed Liverpool at the Stamford Bridge next week Sunday.
One could call Liverpool's scoreless draw with 18th- (now 19th-) place Stoke a hangover after the emotional toll of Tuesday's Champions League semifinals first-leg thrashing of Roma, but in truth the Reds were their typically dominant selves, only without the precision and final touch which have come to define their campaign.
However, Tottenham have a game in hand on Chelsea - they play Watford at Wembley on Monday night, live on Sky Sports Premier League - and Fabregas believes this gives them an advantage over his side.
Fabregas, whose fourth-minute goal was a superb whipped effort into the top corner, echoed Cahill's sentiments.
"When we arrived we were five points to the teams above, we depended on others to try and get out of this position".
"It's a very important game at home and the stadium is going to be packed".
Chelsea also have an FA Cup final date with Manchester United to look forward to next month as they target a positive end to the season following their tame Premier League title defence.
The Reds head to Rome on Wednesday with a 5-2 advantage from the first leg and do so on the back of a tame encounter they controlled for long periods without over-exerting themselves in search of a victor.
"We have had to dig in in certain moments and we are ready to do that".
"We must look to the games that we have - Bournemouth, Southampton and Stoke - to try and achieve the necessary points to stay in the division".
The Nigeria global has featured in 26 Premier League games for the West London club this season and has bagged three goals and assists.
Chelsea have won three consecutive away league games for the first time since September (a run of five).