Giggs wrote in his Sky Sports column that he felt Herrera set a risky precedent by criticising his fellow United players, despite the nature of the shock defeat: "I am a little bit surprised at [Herrera's] comments, though, because you wouldn't really comment about your team-mates, you leave that to the manager".
The Foxes parted company with Craig Shakespeare after the side managed just one win in eight games this season.
The focus will now be on who'll replace the pair at the respective Premier League clubs, and there appears to be no obvious candidate for either position - until now. The Merseyside club spent close to £150m during the summer on new players, but find themselves in the bottom three after a poor run of form over the opening two months of the season.
"Manchester City are obviously still flying with their results and performances but I think they'll have their problems", Giggs told Sky Sports.
"There are a lot of coaches out there who would be interested in those positions".
When asked whether he was shocked to see two big names loose their jobs so early in the season, he said: "I don't think you're surprised in this climate that clubs change managers so quickly. I want to improve clubs and improve players, to enjoy working for them and for players to enjoy the challenge". Giggs believes that there would also be "good jobs" available in the Championship and League One, with "philosophy" being desired above a club's "stature" in the tireless midfielder's eyes.
Giggs chose to take a sabbatical from football but has always said he intends to get into management with an ambitious club.
Everton fans have taken to Twitter to give their reaction to comments form Giggs - most do not want him.
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