The England international was taken off on a stretcher in the 23rd minute at Turf Moor after a heavy challenge from Burnley captain Ben Mee sent Gomez sliding into an advertising board.
Liverpool came from behind to win 3-1, setting a club record for most points 15 games into a league season, thanks to goals from James Milner, Roberto Firmino and Xherdan Shaqiri.
But Klopp was unhappy with the way Attwell refereed Wednesday's intense clash at a rainy Turf Moor.
“I said after the first challenge, I don’t know who did it, sliding tackle from six-seven yards, getting the ball, everybody likes it. I said to the ref ‘it’s no foul but please tell them you cannot do that.’" Klopp said during his post-match press conference.
“Nobody can judge that. You get the ball, nice, but it’s like bowling. Because you get the player as well.
"It happened four or five times, everybody likes it, but Joe is injured, and probably not only a little bit. We don’t know in the moment, we sent him home so we have to see, but it’s his ankle.”
The Liverpool boss admits that aggressive play is part of the game but was hoping to see Attwell take a bit more control of the contest in the interest of safety.
“They wanted to be aggressive," he said. "Aggression is a part of football. You try something, and you need someone to say ‘be careful’.
“There were a lot of situations, challenges. There was nothing to say ‘wow, too much’, they were normal challenges. But with six or seven yards and then [slide], these times are over. They are over.
"We all want to win football games, and there are different ways of doing it. Somebody has to tell you to stop doing it, make two more steps and make a normal challenge. Don’t go five yards before the player because the grass is wet and take any risk.
"It’s not intentional, but these are the situations. The boy with the ball is a bit unlucky because what can happen is what happened to Joe Gomez. I think the referee has to make sure that things like this don’t happen constantly. It’s not how it should be. Let’s play football."
Burnley's opening goal, scored by Jack Cork, had a suspicion of offside while the midfielder tucked home from close range after Ashley Barnes won the ball in a challenge with Alisson.
"I couldn't see that, of course not," Klopp said of the offside decision.
"Not 100 per cent sure but Alisson said to me he had the ball. I don't know what that means exactly, I need to watch it back, I don't know."
Liverpool made seven changes but the introduction of Firmino and Mohamed Salah from the bench with the score at 1-1 was key, victory moving the Reds back to within two points of Manchester City in the Premier League title race.
"Lots of players needed more time to warm up and it was fair, a proper fight," Klopp said.
"They scored their goal from a set piece which does not make life easier.
"Striking them back was exceptional in the circumstances. I really like that, this is massive tonight."