The midfielder landed his first reservation within the first 45 minutes after coming in late on Granit Xhaka.
While his expulsion came at 73 minutes, he came in for 50-50 with the Switzerland international.
Referee Anthony Taylor was quick to show Kovacic a second yellow, who at the time looked a little confused.
But later reruns showed it was a bad decision and Kovacic had every right to be furious as he made his way to the locker room.
And speaking immediately after the challenge, Hoddle took aim at Taylor for showing Kovacic a second yellow.
He told BT Sport: “Getting kicked out for this is ridiculous, it really is.
“Being sent off for that as a second offense, the first one yes of course, but take a second to watch it.
“This is where every former professional footballer knows it’s not a second offense to be sent off. “