The Latics saw their cup dreams dashed at Goodison Park as they came unstuck in their fifth round replay - with substitute Matt Smith offering a solitary reply to efforts from Kevin Mirallas, Leighton Baines and Leon Osman.
Oldham can, however, look back on a campaign which has seen them claim the notable scalps of Nottingham Forest and Liverpool and collect a dramatic home draw with the Toffees.
Philliskirk said: "My feeling is one of pride, first and foremost.
"When we went 3-0 down it would have been very easy for people to be thinking it was going to be four or five but I thought we responded magnificently in the second half.
"Ironically, when they scored the third goal we were probably having our best spell in the game.
"It was disappointing to concede that third but the lads kept going, Matt's got another great goal and I thought we played some smashing stuff in the second half.
"You never know, if we'd got another one it would have been an interesting end to the game."
Philliskirk, who maintains that he has no interest in taking the managerial reins at Boundary Park on a permanent basis, opted to select the experienced Chris Iwelumo ahead of towering frontman Smith - despite the 23-year-old having netted against Liverpool and in the initial tie with Everton.
On that decision, he added: "Chris Iwelumo has been a leader in the dressing room.
"We are a very young team and he has been a voice on the pitch. I am not a ranter and raver. Chris has been an integral part of the turnaround in fortunes in the last three or four weeks.
"It had crossed our mind but lately Matt has been a fantastic impact sub so we decided to go that way. Hindsight is a wonderful thing and I might get criticised for not starting the lad."