A 2-0 defeat at Brighton & Hove Albion ensured that Wolves will play in the third tier of English football next season for the first time since 1989.
Morgan has come in for a large share of criticism from Wolves fans forced to endure back-to-back relegation under four different managers.
The Wolves chairman released a statement this evening which read: "Today is a sad day at the end of what has been an horrendous season; relegation is a devastating blow for everyone who loves Wolves.
"As chairman of the club I take my responsibilities very seriously; we have failed our supporters, and the city, and for that I am truly sorry. Clearly a lot of mistakes have been made over the past two seasons.
"I do not intend to say anymore publicly at this time. As a club we need to reflect on the events of this season and take appropriate measures to move forward. It will not be easy and there will be difficult challenges ahead, but I am more determined than ever to see Wolves prosper and I remain committed to the club."