The Latics are 19th in League One, and had picked up only one point from the eight games leading up to the tie against Brendan Rodgers' side.
Despite the massive upset and biggest crowd at the ground for two decades, the former player turned-manager admitted afterwards that he may not be in charge this time next week.
Latics chairman Simon Corney, meanwhile, has hinted that he is not afraid to let Dickov go, having placed his backroom staff on gardening leave at the turn of the year.
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"It's very awkward. We will have to chat about it tomorrow," Corney told reporters. "Yes, there will be fans who ask how you can sack the manager after this, just as there were fans asking last week how we could keep him.
"Paul has his own decision to make. Days like these are great, but the biggest thing is about staying in this division.
"It's a difficult question. Paul is the first one to say he is under pressure. He knows that, I know that, the fans know that. We have had one draw in our last eight games so there are a lot of things to think about."