Joe Bryan scored a double in extra-time as Fulham defeated Brentford 2-1 after 120 minutes to seal their return to the Premier League having been relegated under Parker in 2018-19.
Fulham’s immediate return to the top flight comes in contrast to the Bees, who were contending for their maiden promotion to the Premier League but missed out.
Parker took over at Craven Cottage in the second half of the 2018-19 season and said there were lessons to learn from that experience, as they begin to plot their way forward in the Premier League.
“You can’t build teams with drastic changes, drastic swings of players,” Parker said.
“This team has been around myself now for the best part of 15 months and they have improved and improved and improved. I’m happy with where we are.
“We are going to need additions. We are going into the biggest league there is but no real drastic changes.
“Some clear errors were made last time and we will learn from that, we need to learn from that.
“We are going into the best league in the world, the best players, it’s a brutal league and I realise the challenge ahead.
“I want to try and enjoy what we have done so far but we need to learn from those mistakes.
“What we’re trying to build and ingrain in the players and this football club is some core foundations.
“If you’re not building your club on concrete but sand, it will be that rollercoaster ride.”
Parker, who made 128 appearances for Fulham as a player, added that promotion made him emotional having been in charge for their relegation two years ago.
“I feel emotional, the journey you go on, the ups and downs along the way, the disappointment,” he said.
Brentford counterpart Thomas Frank will be hurting, with the Bees coming close to automatic promotion before losing their final two league games of the campaign.