The Latics are back in the League One relegation zone thanks to second-half goals from Michael Doyle and Dave Kitson.
But Philliskirk said: "There wasn't a lot between the sides, but we made two individual mistakes and got punished both times.
"It's disappointing, but we had a real go and we should have had an unbelievably blatant penalty for a push on Robbie Simpson.
"It isn't nice being back in the bottom four, but we already knew we had some massive games ahead of us and that we needed points as quickly as possible.
"It isn't panic stations and there were positives to take from a very difficult game against a very good side.
"I've seen a lot of Sheffield United this season and they are the most efficient side in League One - I'll be absolutely gobsmacked if they don't go up.
"For us, it's about getting a result at Tranmere next Saturday and winning games against the teams around us."
Philliskirk confirmed that Oldham's regular goalkeeper, Dean Bouzanis, had been dropped for disciplinary reasons.
He added: "It's an internal matter that has been dealt with, and that's the end of it."
