Struijk was dismissed for a challenge on Harvey Elliott that left the Reds midfielder with a dislocated ankle.
Elliott, 18, had surgery on Tuesday but could play again this season.
The Liverpool player disagreed with the upholding of the 22-year-old's ban, calling the decision "wrong" in a reply to an Instagram post.
Struijk will miss games against Newcastle United and West Ham United in the Premier League and Fulham in the Carabao Cup.
He will be available again for the league game against Watford at Elland Road on 2 October.
Struijk had earlier apologised to the teenager for the challenge on social media, saying he was "gutted" and "never meant for it to happen".
Elliott replied to a previous Instagram post to say the centre-back had nothing to apologise for, describing the incident as a "freak accident".