Club captain Morgan was recalled after five games on the bench by new Foxes boss Brendan Rodgers, who took charge of his first match back in England, and fingers have been pointed towards Morgan for his role in the 2-1 defeat.
The 46-year-old took over from Claude Puel at the King Power on Tuesday, ending his 32-month stint at Celtic.
The Foxes leveled in the 75 minute as striker Jamie Vardy outpaced Leicester's defense to slot home calmly, setting up a tense finale.
A draw seemed fair but, in added time, Gray ran on to Deeney's reverse pass after a Leicester clearance had been headed back towards the danger zone and finished coolly to spark wild celebrations in the stands. "It is an important amount of points for us, but I can feel the players want more and more".
Asked if he could return to Celtic as manager, Northern Irishman Rodgers said: "Yes".
His 121nd strike for the club got the Hornets up and running and he showed finesse to play a brilliant ball for Gray to win the points in the 92nd minute for Javi Gracia's side.More news: 'Strange' if I'm not at Man United next season, says Solskjaer
He said: "The goal at the end is a case of managing the game".
"I made a lot of good friends down there".
As for the summer, Rodgers believes that he will have the support of the Leicester brass, saying: "There is no doubt we will look to improve, but there is no figure, no number".
"I was pleased with the spirit of the team". I said whatever the result, for me, I only wanted to see spirit and intensity and I saw that.
"It would be great to have that opportunity going into the last couple of games".