Fulham have been relegated from the English Premier League in their first season back up after a disappointing 2-0 home loss to Burnley on Monday.
The Cottagers already needed a miracle from their final four games to stay, but the defeat to fellow relegation contenders Burnley mathematically sealed their fate.
“I’m hurt, I’m gutted. The players are (too),” Parker said post-game.
“Everyone has tried everything possible, everyone at the football club has done everything in their power to try and stay in this division this year.
“What’s important is were going to have to have these honest conversations about what we need to do. Well do that together, and well try and bounce back.
“There’s been disappointment this year, and we need to put our hands up, we need to get around a table, we need to understand where we want to go as a club, what we need to do.”
Fulham joins West Bromwich as newly promoted clubs going straight back down but they will be buoyed by Norwich City and Watford’s promotions from the Championship this season after relegation last term.
Parker added: “Ive nothing but full respect for my group of players and what theyve given me this year, in terms of effort and endeavour daily, wanting to improve, wanting to get better, but the facts are that weve fallen a little bit short with our quality, hence why weve been relegated out of this division.”