The Hammers keeper needs no reminding how tough the Premier League is after being part of a Swansea side relegated last term.
Fabianski, who was thrown a top-flight lifeline after joining for £7m, is among a host of summer signings at the London Stadium.
West Ham shelled out a club-record £40m for Felipe Anderson while Jack Wilshere and Andryi Yarmolenko have also joined.
There is a renewed air of optimism under new boss Manuel Pellegrini but Fabianki has played down the increased expectation.
He said: “You can see there is quality in the group.
“Hopefully we’ll get better and better with every single game and will be ready for the season.
“But you can’t get carried away. There’s a few new players here and we are getting used to playing with each other.
“You have to be prepared for all the different periods you’re going to go through.
“Going down was not the ideal way for me to leave Swansea.
“It’s not the best feeling to have, but the Premier League the toughest competition and you have to be ready for almost anything.”
Ex-Arsenal stopper Fabianski, 33, will battle it out with Adrian to become No1 under Pellegrini.
The Pole hopes to stake his claim in the two-match tour to Austria as preparations are ramped up for the opener against Liverpool on August 12.
Fabianki added: “We will put in more work on the tactical side of the game and then try and just getting sharper and sharper.”