Latics bowed out at the fifth-round stage of the competition with a battling 3-1 replay defeat at Everton on Tuesday night.
Results elsewhere mean the Lancashire side head into Saturday's home game against promotion-chasing Sheffield United a point and a place above the relegation zone despite three consecutive league wins.
"That's what we said at the end of the game, enjoy this, have a day off tomorrow and come in on Thursday ready to work," said Philliskirk. "We've got Sheffield United on Saturday, which is a massive game.
"The players should take a massive amount of confidence from the second-half performance at Everton. They've got to transfer that onto Saturday-Tuesday in the league and hopefully get us away from trouble as quickly as possible and survive in League One."
Captain Dean Furman echoed Philliskirk's sentiments.
"It's massive," he told Press Association Sport. "The league is our bread and butter and it's vital that we remain in League One.
"We know that the task is going to be a difficult one. We're out of the relegation zone. Results didn't go for us (on Tuesday) but we have a game in hand.
"As we've shown over the last few weeks, we can pick up results. We're on a great run of form in the league and we'll look to continue that on Saturday.
"We're playing with a lot of confidence at the moment. I know we lost to Everton but we're not going to let our heads drop too much. We know we've got a difficult task ahead of us but we're prepared for it and we're looking forward to Saturday."