The violent scenes caused last night's kickoff to be delayed by 45 minutes, and overall it was a disappointing night for the Red Devils as they suffered a 3-2 defeat.
This morning on Sky News, Holmes, who is a United supporter, said on air: "This is going back to the '70s and '80s. Everything that you were seeing that was bad about Hillsborough for instance."
It was also concluded that the supporters were not to blame for the crush, which was caused by overcrowding in the Leppings Lane end of the stadium.
After making the comments, Holmes tweeted: "Just being made aware of someone trying to use me to stir up trouble re The Hillsborough disaster. How low, how disgusting. The Hillsborough families have suffered enough without distasteful sniping like this.
"For the record there is no comparison between events last night at West Ham and Hillsborough. On the programme I was trying to talk about images we never ever want to see again. If anyone concluded anything different my humblest & most honest apologies. I am a huge supporter of The Hillsborough struggle for justice. Last night's events do not remotely register in comparison.
"I am an honest & decent football supporter & man & would never seek to create such an offence. Those who are trying to do so r very wrong. Obviously there is no comparison between Hillsborough & the scenes at W Ham last night. I apologise unreservedly if anyone thought I was making that connection."
Meanwhile, West Ham have vowed to issue life bans to the supporters who were involved in last night's attack.