The England goalkeeper was speaking before last night's home defeat to Manchester United.
Pickford said: “When I joined we were in Europe, we know the history of Everton Football Club, there's a lot of fantastic history, a lot of trophies won, a lot of titles won, and it's how do we, as Everton players, now create our own history?
“We've seen over the last couple of years Crystal Palace winning the FA Cup and getting into Europe, Nottingham Forest getting into Europe.
"I know they're not having the best of seasons but they got into Europe, they were close to getting Champions League football last season, we've seen Newcastle winning the League Cup when they've not won a trophy for a long time.
"The opportunities are there, it's about taking them and grasping them with both hands when you get that opportunity.”