The LaLiga champions saw Antoine Griezmann sent off and a penalty in their favour overturned after a VAR check as they fell to defeat in the Champions League clash.
After the game, the Argentine boss sprinted straight down the tunnel refusing to shake the Liverpool manager's hand.
Diego Simeone refused to shake Jurgen Klopp's hand after Atletico Madrid's 3-2 defeat
The Atletico manager quickly hurried down the tunnel after the final whistle against Liverpool
Klopp was seen holding out his hand and then gave a thumbs up when Simeone ran down the tunnel before he shook the hands of the Atletico's players.
BT pundits Peter Crouch and Joleon Lescott were both disappointed that the Atletico manager didn't shake the Liverpool manager's hand.
Former Liverpool player Crouch said: 'I respect him so much as a manager Simeone but I just think during the game, winding the crowd up, winding the players up, I understand it, but then not shaking hands at the end he lets himself down.'
Lescott described Simeone as 'petty' for his refusal to shake hands.
The ex-Manchester City defender said: 'I think it's petty. He handled himself well yesterday in regards to the remarks Jurgen Klopp made before the game but he didn't seem phased by it.
'But then not to shake his hand and then run off up the tunnel was a bit cowardly in my opinion.'
After their most previous meeting in which Atletico knocked out then holders Liverpool in the last 16 of the Champions League in 2020, Klopp questioned why the Spanish side had not played 'proper football'.
It was a good night for Liverpool who took their third win in three Champions League games
Antoine Griezmann scored a brace to pull Atletico level but was then sent off for a high boot
Klopp says his comments were based on emotion at the time, with the match Liverpool's last prior to the coronavirus pandemic causing a suspension to the football calendar.
The German did add though that he respected Simeone but wasn't a fan of Atletico's style of play.
When asked about Klopp's comments before the game on Tuesday evening, Simeone refused to comment.
Atletico then gave away a penalty and had one of their own overturned in a bad night for Simeone's side
Liverpool boss Klopp played down Simeone's refusal to shake his hand during his post-match conference.
He said: The situation is clear I wanted to shake his hand, he didn't want to so his reaction was like mine (in 2020) was not too cool but we are both emotional so we will see each other next time and shake hands definitely and it's nothing.
'He obviously wasn't happy, not with me but with the game and it's nothing else.'
During the group stage match, Liverpool took a 2-0 lead through goals by Mo Salah and Naby Keita.
Jurgen Klopp played down Simeone refusal's to shake his hand during his post-match conference
Griezmann then bagged a brace to level the score but was sent off after 52 minutes for a high boot on Roberto Firmino.
Atletico held out until Mario Hermoso gave away a clumsy penalty for a challenge on Diogo Jota, which led to Salah bagging his second goal to give Liverpool a 3-2 win.
Jota then appeared to give away a penalty after a challenge on Jose Maria Gimenez only for VAR to overturn the decision.
Liverpool now sit top of the group with nine points, and a win against Atletico at Anfield would be enough to see them qualify.
The Spanish giants sit second in the group level on points with FC Porto who took a 1-0 victory over AC Milan.