"I'm sorry that we let you down," Khan said on Wednesday in a statement on the club's website.
"Our goal this season was to build on what we achieved in promotion and deliver on our pledge to invest heavily in the squad, ensuring that Fulham would always compete in the Premier League and, no matter the result, never disappoint.
"Last night's outcome made official what we didn't think would be possible in August and tried desperately to remedy and avoid as the season wore on."
The club spent an estimated 100 million pounds ($131.79 million) on new players in the close season after gaining promotion to the top flight.
But they failed to click as a team, even naming three managers over the course of the season with Slavisa Jokanovic being replaced in November by Claudio Ranieri, who was then sacked in February and succeeded by interim coach Scott Parker.
"We hold ourselves accountable," Khan added. "We will reflect, plan thoroughly and respond accordingly. In the weeks ahead we will communicate further as to our vision for the future."
Fulham, who have the worst defensive record in the league having conceded 76 goals in 33 games, could still finish bottom with Huddersfield only three points behind with a game in hand.
(Reporting by Rohith Nair in Bengaluru; Editing by Christian Radnedge)
