The Giants moved to second in the Super League table as a late Danny Brough try helped them hold off their opponents in sweltering conditions at the KC Stadium. However, Anderson did not hold back in the post-match press conference when he labelled the big tackle by Ellis that left the Huddersfield scrum-half flat out on the field as a shoulder charge.
Anderson said: "The tackle was a straight shoulder charge to the head. He's not knocked out for no reason. There are five people out there, one with the whistle, two with the flags and two muppets that stand at the other end of the field that don't see anything."
He added: "It's a stone-cold shoulder charge to the head. I'm like Peter Gentle last week when Justin Poore dropped somebody on his head. Nothing will get done about our one, straight right shoulder to the head, it's a penalty. Luke is coming round; he knows he's in Hull at the minute."
Hull FC coach Peter Gentle counted Anderson's claims, saying: "I just had another look at Gareth Ellis' tackle on the video. He [Paul Anderson] better come and have a look at the video I've got. I didn't see anything wrong with it, not at all."
The win for the Giants came courtesy of solid defensive work on their own line, something Anderson admitted he was pleased about.
"We weren't so great today but we found a way to win," he added. "What we have done is a lot of practice on our try-line defence, and from today you can certainly tell. Defensively we have been outstanding all year."
For the home side, Gentle believes they are heading in the right direction despite four defeats in a row in Super League.
"If we would have played like that in the last two weeks we would have got the results," said Gentle. "We've still got too many basic errors in us and our attack is still mis- firing. We talked at half-time about what we were supposed to be doing. We couldn't generate any speed of the play of the ball in the first half.
"We started the second half better and got some field position and if a few things could have gone our way it might have been a different result."