The Cottagers were promoted back to the Premier League on Tuesday after beating Brentford in the Championship play-off final at Wembley.
"There were some clear errors made last time," Parker said.
"We will learn from that. We need to learn from that.
"We're going into the best league in the world, the best players, the best teams… it's a brutal league and I realise the challenge ahead.
"What we're trying to build and what we're trying to engrain in these players, in this football club, is some core foundations.
"Sometimes those core foundations get you far in life. You can have as much talent as you want but, if you're not building your football club on concrete and you're building it on sand, then in the end it will be the rollercoaster ride.
"I hope we can grow gradually. It's going to be tough but, if we can't, we have core foundations that we always fall back on."