The Bluebirds were relegated after just one season in the top flight on Saturday as a 3-0 defeat at Newcastle United condemned them to life in the Championship.
When asked if he thought that the team could achieve promotion again at the first attempt, Whittingham told Sky Sports News: "Yes. Most of the boys here got the club up, so we've got the core of it. We'll see what the manager does in the summer and everybody will go from there.
"It's a very tough league and it shows up if you're not good enough. Everyone needs to go back to the drawing board, start again, and hopefully get back here."
Cardiff wrap up their Premier League campaign next Sunday when they entertain title challengers Chelsea.