Keane has become well-known for being an outspoken pundit since joining Sky Sports.
The former midfielder is known for his outbursts, and has angered Jurgen Klopp in the past with his criticism.
Klopp was quick to respond, and joked that Keane must have been watching a different game.
And Holloway believes Keane has always looked to aim a quick jab at Liverpool whenever he has the chance to.
The former Plymouth manager expressed to The Sun that Premier League managers are always the first to get criticised despite the lack of fans in stadiums.
He said: “I take my hat off to all of them because I understand the pressure of how you might feel because of the media. The media cause a lot of this.
“There’s no fans but they’re on at you all the time at that level.
“There’s also a part of learning how to deal with them.
“I thought Jurgen Klopp last night was magnificent in dealing with what happened and the game and how proud he was of his team.
“Because he’s lost some major, major players. And Man United haven’t really lost any of them yet.
“I found it interesting because Roy Keane annoyed me a bit yesterday.
“He’s all ‘we’re doing well again’ and he couldn’t wait to get a dig in at Liverpool.”