Llambias has also confirmed that he and Ashley will hold talks this week with Alan Shearer over the club's future with the former Newcastle skipper's term as interim manager officially ending today.
The former casino boss, who runs the club on a day-to-day basis for the sports retail tycoon, spoke out after Newcastle were condemned to Championship football when they lost 1-0 at Aston Villa.
"Being relegated from the Premier League is a huge disappointment for everyone involved with Newcastle United," Llambias told the club's official website in the wake of relegation.
"We are all hurting and I feel desperately sorry for everyone associated with Newcastle United; for Mike Ashley, who has invested heavily in the club, and for all the supporters who have given the team magnificent backing up and down the country all season long.
"Mike and I will sit down with Alan this week to discuss how the club moves forward again, and I hope to be able to say more to our supporters later this week."