Before the Premier League clash, Klopp said it was a "waste of time" attempting to persuade the football authorities and broadcast rights holders to review the fixture schedule after Liverpool played the early Saturday fixture at following their Champions League defeat to Atalanta on Wednesday.
When asked by BT Sport whether Milner suffered a hamstring injury, Klopp replied: "Yeah, congratulations. Hamstring. Surprise. And they had injuries as well because it's a tough time."
"I don't know how often I have to say it. You picked the 12:30 [p.m. GMT]. These are difficult moments. If you play at 15:00 or 17:30 [p.m. GMT] it's exactly the same. I'm not having a go at the broadcasters, I'm just saying how it is.
"Wednesday to Saturday at 12:30 [p.m. GMT] is very dangerous for the players. It's not only my players who have that problem. I only go for the broadcasters with the Wednesday to Saturday at 12:30 [p.m. GMT].
"I wanted to stop doing it because it doesn't help. It's a bigger problem this season, because of the short preseason and things like this. We have this slot three times. Look who else had this slot three times? No-one."
Premier League matches can start as early as 12:30 p.m. GMT with other slots at 3 p.m. GMT, 5:30 p.m. GMT and 8 p.m. GMT.
Klopp also criticised Sheffield United boss Chris Wilder who openly opposed the reintroduction of five substitutions.
"Chris Wilder or whoever, constantly say I'm selfish," Klopp added. "I think all the things show that he's selfish but that's not too important.
"I was in a similar situation as he is when I worked at Mainz -- all about staying in the league. They now have three subs and one point."
Brighton earned a draw when they were given a stoppage-time penalty after referee Stuart Attwell was sent to the pitchside monitor and ruled that Andy Robertson had caught Danny Welbeck. Liverpool also had two goals from Mohamed Salah and Sadio Mane ruled out for offside by VAR.
"I don't want to speak for anybody else but in my opinion I would. I just want to play football as normal," Henderson said.
"I saw Kevin De Bruyne saying in an interview they have changed so many rules we don't know what they are anymore. That for me is a big problem. We are talking about instances all the time and not the football. In my opinion I would rather play without it.
"If they're offside, you do the line thing, then what can you do? The third one, I don't know, it's not a penalty.
"You can think I'm biased but if you ask four or five or their lads they will say the same thing... You feel as though there are a lot of decisions that go against you, but that decision for me today is baffling."
Information from Reuters was included in this report.