The England goalkeeper moved to Selhurst Park after coming off contract at West Brom.
“Twenty-nine for goalkeepers is coming into your peak, and that's where I am at the moment," he told Palace TV. “I had my loans growing up, and then did my first permanent move to West Brom for the last four years which was great, and now it's time to do another step and go again.
“It's a great opportunity for the lads to take on what they did last year into the new season and get higher up the table. The lads will have loved doing well last year, being a success and finishing in a good position in the Premier League.
“But as footballers, you want to better yourselves. I think that will be an aim for everyone at the club, all the players and the staff, to do it again – and better."
Johnstone, who has signed a four-year deal, feels he can fit in with Patrick Vieira's possession based style of football, and that competition from a particularly strong goalkeeping unit at Palace can drive him on.
“I met the manager, which was good," he said. “I hear all good things about him and can't wait to work under him.
“Everybody now is wanting to play football, and I think last year [Palace] did it and were good at it. It's something the modern day goalkeeper needs to have in the locker as well. It's something we did at West Brom over the last few years, so hopefully I can settle straight in with that as well.
“As everyone knows, the goalkeepers are together, separate [from the main group] most days, so you need to push each other and support each other. I feel like that's what this group has.
“Obviously Dean [Kiely] the 'keeper coach will implement that as well. The lads are working hard, pushing each other but having a good time at the same time."