Mourinho's side play Dynamo Kiev at Stamford Bridge on Wednesday night, seeking a second home win from two attempts after the opening 4-0 defeat of Maccabi Tel-Aviv.
Defeat at Porto followed in round two and a draw in Kiev against still unbeaten Dynamo last time out means the Blues are third in the group with three matches to play.
Mourinho has previously insisted Chelsea, who have struggled in defence of their Barclays Premier League title, are not a Europa League club, despite winning the trophy in 2013 after becoming the first European Cup winners to exit at the group stage in defence of the trophy.
That was under Rafael Benitez, an interim appointment after the departure of Roberto di Matteo.
It is feasible a similar fate could await Chelsea this term, with Mourinho under pressure for an about turn in results.
Chelsea must beat Dynamo on Wednesday night or risk falling into the second-tier competition Mourinho has derided so often, despite winning it himself with Porto in 2003.
The 52-year-old Portuguese is bidding to become the first manager to win the Champions League with three different clubs, having triumphed with Porto in 2004 and Inter Milan in 2010.
The trophy proved elusive in his first spell at Chelsea and while at Real Madrid and Dynamo could do some damage on the break in west London.
Sergei Rebrov's side were dangerous at the NSK Olimpiyskyi after Eden Hazard and Willian had hit the woodwork for Chelsea.
Mourinho afterwards was aggrieved Chelsea had not been awarded a penalty for a foul on Cesc Fabregas which went unpunished, but maintained Chelsea were still in control of their Champions League futures.
He said: "The result is acceptable because it keeps us in a strong position.
"We have the game at home (against Dynamo), Dynamo plays against Porto so they have to lose points.
"We are third, but we are in a stable position."
Chelsea still must play Maccabi Tel-Aviv in Israel on November 24 and Porto on December 9, but the Dynamo clash is key.
Source : PA