Liverpool boss Andoni Iraola said it is a "shame" there is no reward for honesty after his side were controversially denied a penalty in a 1-0 defeat to Arsenal on Sunday.
The defending Premier League champions moved to the top of the table and nine points clear of Liverpool after their first win at Anfield in 14 years.
But Liverpool were left aggrieved after Alexander Isak was pulled back by Jurrien Timber as he attempted to meet Bradley Barcola's cross midway through the first half.
The Swedish striker did not go to ground and, as a result, neither the referee nor VAR intervened to award a spot-kick.
Timber could even have been sent off for denying a clear goalscoring opportunity without attempting to play the ball.
"It's a shame you ask me this question. But honestly, yes, we have to tell them to go down because they are not going to call it otherwise," said Iraola after only his second defeat since taking charge of the Reds.
"I don't see the reason why. Only because he hasn't dived or he hasn't gone to the floor. It shouldn't be a reason, but of course it's a penalty."
Arsenal led by the time of that contentious decision through Kai Havertz's early opener.
Liverpool roared back and should have been level by half-time as Florian Wirtz curled a free-kick off the crossbar and Alexis Mac Allister headed a glorious chance over.
"We had good chances - we hit the crossbar and had good situations we were not able to finish. We definitely deserved a goal," added Iraola.
"I loved the reaction from my players after going 1-0 down...I loved a lot of moments of the game.
"We have to keep going. It is very early in the season. Arsenal are in the best of the situations, but it is just the start of November today."
Victory could be a giant step towards retaining the title for Mikel Arteta's men.
The Gunners move three points clear of Manchester City at the top of the table.
But with City expected to be hit with a huge points deduction unless they overturn a guilty verdict on more than 100 charges of breaking Premier League financial rules, Arsenal dealt a major blow to one of their most realistic title rivals.
Arteta was delighted by his side's reaction after bowing out of the League Cup in embarrassing fashion to fourth-tier Fleetwood on Tuesday.
"After the defeat against Fleetwood, it looks like the end of the world; it looks like what are we doing? Then you have to pick yourself up and understand that this is the beautiful part of this game," said Arteta.
"The mission was something that we didn't accomplish in 14 years and there were reasons for that.
"Some of them were psychological problems, some of them were related to the quality that we showed on the pitch, certain moments or decisions and we needed to nail absolutely all of them."