Latics secured a place in the FA Cup quarter-final draw at the weekend when Matt Smith came off the bench to net a stoppage-time equaliser against Everton.
Oldham's fellow strugglers failed to capitalise on their absence from league action and victory over Boro will move them out of the relegation zone.
"I said to the players after the game, 'enjoy tonight but - capital B - Tuesday night, it sounds silly, is just as important'," said caretaker manager Philliskirk, who is undefeated in the two games following Paul Dickov's resignation.
"The way results have gone at the weekend in the league, if we can win at Stevenage we're out of the bottom four.
"With what I saw on Saturday, the spirit, if some one walks in on Monday or after the Stevenage game he's going to inherit a team that, in my opinion, has a lot more to offer and are better than the league position suggests."