The England international was injured in a challenge from Adam Le Fondre in the opening minutes of Everton's 3-1 win over Reading on Saturday at Goodison Park.
He had to be immediately replaced, and Moyes said: "I genuinely haven't seen it again but I thought on the pitch it didn't look good.
"Jagielka knew about it and it is a bad one. He will have surgery tonight [Saturday] to stitch up his ankle.
"It is a bad one because he is a key player for us."
Moyes said he did not know how long Jagielka would be out but the 30-year-old must now be doubtful for next week's FA Cup quarter-final against Wigan.
The incident also reminded Moyes of some of the treatment goalkeeper Tim Howard received in the two previous cup matches against Oldham.
Howard was unable to face Reading after suffering a knock in the fifth-round replay win over over the League One side on Tuesday and was replaced by back-up Jan Mucha.
"I'm not happy with the challenges on the goalkeeper in the last two games that have put him out and I am not happy with the challenge today [Saturday] that puts Phil Jagielka out," said the manager.
"I'm not one who minds challenges. I like a bit of that, if that's what it is.
"I don't mind robust challenges but not one that puts out arguably one of my best players."
Howard's absence ended the American's run of 210 consecutive Premier League appearances.
Moyes said: "I thought Jan did very well but it came about because the goalkeeper wasn't protected in the first game against Oldham and they felt it was right they could do that again in the second game.
"In the end the goalkeeper has been injured because of decisions which should have been deemed free-kicks long before."
Reading manager Brian McDermott also said he did not get a clear view of Le Fondre's challenge on Jagielka but defended his player.
McDermott said: "Adam Le Fondre is not that type of player, no way. He is a very honest type of player.
"I don't know what they are saying but there is no way Adam Le Fondre is a player that would 'do' anybody."
Jagielka will certainly hope to be fit to take his place in England's squad for their next World Cup qualifiers, against San Marino on March 22 and Montenegro four days later.
When pressed, Moyes later said Jagielka could be out for "a couple of weeks, maybe".
Le Fondre apologised after the game, saying via Twitter: "Fans were brilliant today! Shame about result! Everton were class! Thoughts with jags never meant to catch him,caught him late an apologised."