The hosts felt the Reds' first goal of the evening through Sadio Mané on 17 minutes was contentious, complaining that the ball crossed the line for a goal-kick before Joe Gomez's cross although the linesman refused to raise his flag.
But their biggest grievance understandably came when visiting goalkeeper Simon Mignolet only received a yellow card for bringing down Mame Biram Diouf on the edge of the box as Liverpool's last defender.
Mohamed Salah scored twice from the bench late on to add to Mané's opener and put the Potters' hopes of a result to bed, but Hughes felt the defining moment came when Mignolet remained on the pitch.
Mignolet foul "clearly a goalscoring opportunity"
"That's the key moment in the game from our point of view," said the Welshman when asked about Atkinson's decision not to send Mignolet off before half-time.
"I just don't understand why the referee and the officials couldn't see that for what it was; clearly a goalscoring opportunity. If the 'keeper doesn't wipe Mame Diouf out, it's a tap in into an empty net.
"At that point it's 1-1 and game on. It came at a time when we were in the ascendancy and asking questions of them.
"We went behind to a poor goal from our point of view, which was a little bit contentious as well. We felt the ball had gone out, I'm not sure if it did.
"Usually as the home team you get the benefit of the doubt in those situations and I don't think we got the benefit of the doubt from the officials on too many occasions tonight to be perfectly honest.
"It is what it was. We just needed to keep going, which I felt we did, we were very much in the game at 1-0 down. We kept on asking questions of them."
The Stoke boss insisted that Salah's late brace was a result of the hosts having to chase the game rather than an indication of any deeper-lying defensive issues - despite having conceded a league-worst 29 goals this term - and felt the score-line was kind on the Merseyside outfit.
He added: "Obviously it's a high-risk strategy and you're always going to be susceptible to counter-attacks, and given their talent and pace at the top end of the pitch, that can be an issue for you.
"In the end the second goal is a great strike from the lad, he's only just come on and he's been doing that all season so you have to hold your hands up sometimes when a quality strike like that takes the game away from you.
"The third one is just tiredness and individual errors, that's a little bit hard on us, in terms of the margin of victory for Liverpool. I don't think it was a 3-0 defeat. It's frustrating.
"The one thing you want from the referee and the officials is to get the big moments and the key match-defining decisions right. In my view, he didn't tonight unfortunately."
Hughes left feeling let down by refereeing decisions
Joe Allen twice went close in the second half with Stoke failing to take advantage of their sparse goalscoring opportunities and producing just one shot on target - in the 91st minute.
On Allen's chances, Hughes continued: "We needed them to go in, clearly. The first one, when he side-footed it, that's clipped somebody as it's gone through.
"The other one from [Peter] Crouchy's header, he just couldn't get over the top of it. We needed one of those to go in to get back on level terms. If we had have done then who knows, it might have been a different game and a different result maybe.
"Credit to Liverpool, they're a very strong side. You look at the talent that they had on the pitch to begin with and they made a lot of changes and they've got the luxury of being able to bring a lot of talent off the bench as well, so you have to deal with that when that happens.
"It's disappointing that we got beaten 3-0 but you need the officials to help you sometimes when you go up against the big clubs."