The League One outfit head to Goodison Park on Tuesday for the fifth round replay after their initial meeting at Boundary Park ended 2-2 thanks to a very late equaliser from Matt Smith.
In the fourth round, Oldham eliminated Liverpool from the famous cup competition and now Wesolowski is targeting the scalp of the Anfield clubs Merseyside rivals.
"Realistically, we know it's going to be tough but all the expectation and pressure is on them now more than ever.
"We will try and keep it at 0-0 for as long as possible and try and nick one on the break.
"It's the magic of the FA Cup and anything can happen, as we have already seen in knock out competitions this season with Bradford reaching the League Cup final and Luton knocking Norwich out of the FA Cup."
He added: "Our win over Liverpool was also a big shock to many. But not so much to us. We just knew we could produce something special against them.
"And if we can get past Everton, then we'd fancy ourselves in the sixth round at home to Wigan."