The Barclays Premier League side came from behind to go 2-1 up against their npower League One hosts through Jagielka's 48th-minute header, before seeing Latics substitute Matt Smith salvage a replay by nodding in a stoppage-time equaliser.
Reflecting on the Toffees' display, Jagielka told the club's official website: "We created a couple of chances in the second half but we didn't manage to test the goalkeeper or the final ball wasn't quite good enough.
"We were on top after we got the second goal but we needed to get that third. Unfortunately we didn't and fortunately for the neutrals and Oldham fans it stayed at 2-1. Then they got the great header to equalise.
"Obviously going down the hill (in the second half), they put us under a bit of pressure. We had quite a few experienced players out there but we started to panic a little bit. Clearances didn't go where we wanted them to which could have bought us a bit more time.
"It wasn't to be, that was the way the game went. The manager (David Moyes) wasn't very happy but at least we are still in the cup. Hopefully we will put in a better performance (in the replay) at Goodison Park."