The Toffees have come close to cup success in recent seasons, with Wembley defeats to Chelsea and Liverpool dashing hopes of silverware in the latter stages.
Baines has insisted that he has no regrets about joining Everton and has challenged his side to end their trophy drought in May.
He told ITV Sport: "I probably took a little bit of a gamble joining Everton but it just felt right, it was the only place I wanted to go.
"David Moyes has got his team set up in a way that we can do anything, teams aren't quite sure which approach we will take.
"It just makes you hungrier to get within touching distance. We are at that exciting stage of the competition, we have to look back at that moments that hurt and use them as motivation."
Baines's former club Wigan Athletic travel to Everton today in the FA Cup quarter-finals, with the winner guaranteed a trip to Wembley in the last four next month.