Rebic opened the scoring in the second half when he capitalised on a Willy Caballero error to volley past the goalkeeper before Luka Modric and Ivan Rakitic completed a resounding win as Croatia booked their spot in the last-16 of the World Cup.
Croatia defender Sime Vrsaljko taunted the Argentina players for their reaction to the loss, saying they were "crying like girls", and Rebic was even more disappointed with Messi and Co.
"To be honest, I wanted to get Messi's jersey for my friend, who is a big fan of Leo," the 24-year-old player told Goal. "But the Argentines made such a bad impression on me that I gave up on asking Messi for his jersey.
"Honestly, I expected much more. At least of those players from the Premier League, who are used to a high tempo and duels. You saw Nicolas Otamendi - in the fourth minute Mandzukic passed by him and he was rolling on the floor. I am disappointed by their behaviour and lack of fair play, not to mention how they provoked us. An athlete should know how to deal with defeat."
The Eintracht Frankfurt player moved his criticism on to referee Ravshan Irmatov, suggesting the Uzbek did not have enough experience at the top level to run such a game.
"The referee was not of a quality level and it is not the first time it has happened at the World Cup, with many referees without experience in some of biggest competitions like the Champions League.
"We felt a lot of decisions went Argentina's way, so I was sure he wasn't going to show me a second yellow card. I appreciate this is the World Cup and you have to have referees from all over, but it's important that these matches be led by referees who can match the importance and the pace of the match. For example, the referee didn't even have football boots but only regular sneakers! That shocked us.
"I feel sorry to be nervous about some referee's decisions now rather than enjoying my goal and the fact we smashed Argentina. When Otamendi deliberately kicked Rakitic with the ball, that was clear red card. But, it only makes our victory sweeter."
Rebic scuppered an opportunity in the first half when he sent an effort wide of the target but recovered shortly after the break, and was delighted to see the ball hit the top corner of the net after Caballero's wild pass fell perfectly for him.
"I don't even know how many messages I received after the match!" he added. "This was the best game I've played for Croatia and, along with the recent German Cup final against Bayern, the best in my career.
"I've looked at my goal 100 times by now. Turned out pretty good, didn't it? I thought defenders would catch me if I was to bring the ball down and control it before shooting, so I shot first time without thinking much.
"I had big chance at the end of first half. I did everything wrong: first touch, shot, I didn't pass the ball... Luckily the half-time break arrived, I needed it to pull myself together.
"After the Nigeria game we didn't celebrate much. I spent most of the time at the doping test, but this time we celebrated in the locker room, the bus, the plane... But, we shouldn't stop here, now that we've passed the group stage."