Perisic put in an impressive display in Nizhny Novgorod on Thursday, as Willy Caballero's error – which gifted Ante Rebic the opener – and goals from Luka Modric and Ivan Rakitic secured Croatia a place in the World Cup knockout stages for the first time since France 1998.
Messi was well marshalled by Croatia throughout, and Inter winger Perisic says that Argentina must learn to work together if the 30-year-old is to reach the levels that Portugal's Cristiano Ronaldo manages in major tournaments.
"Messi is the best, just like Cristiano Ronaldo, but you can only achieve something if you play as a team," Perisic told Mediaset.
"Argentina need to change something if they are to go forward.
"As for us, we're on the right track to emulate what we did in France '98 and must continue like this.
"We did really well. In the locker room, we said that we had to defend stoutly and we did that.
"We had chances in the first half too, then the goals arrived after the break. We have six points, we deserved them and now we want to beat Iceland too."
A point against Iceland would be enough to secure top spot for Croatia in Group D, and ensure that a tie with likely Group C winners France is avoided in the next round.