Messi cut a frustrated figure throughout Thursday's clash in Nizhny Novgorod, as Willy Caballero's calamity paved the way for a convincing Croatia victory, putting Argentina in real danger of a first group-stage elimination since 2002.
Caballero may have gifted Ante Rebic the opener, but Modric needed no help with scoring Croatia's second - a wonderfully dispatched finish from distance.
Ivan Rakitic wrapped up the win in style late on, and man of the match Modric was adamant that Croatia must be praised for keeping Messi on the fringes of the game.
"I don't want to comment too much on other players' games. We're happy with how we're playing," Modric, who also scored from the spot in Croatia's opening win over Nigeria, said.
"This result and Argentina's poor display was due to our good game, our compact block all over the pitch, especially when we didn't have the ball.
"In the first half when Argentina had the ball we cut off Messi, he's the most dangerous player. We cut off the passing lines, we wanted to stop Messi receiving the ball and that's how we cut out their creativity. They had one or two chances but from our mistakes.
"We missed three clear chances but everything opened up in the second half, particularly after Caballero's mistake. We scored two more beautiful goals and we won deservedly."
Croatia are now guaranteed a place in the last 16, and a point in their remaining fixture against Iceland - who will be in pole position to progress over Argentina should they beat Nigeria - would ensure top spot.
It is an achievement that Modric does not underestimate, with Croatia having failed to qualify for the knockout stage since France 1998, when they finished third.
"Our most important was achieved, we're ecstatic. I think we should go game by game. Let's not get ahead of ourselves," Modric said when asked if this side could repeat the feat of 20 years ago.
"This will boost our confidence. We're expecting to do great things but I must reiterate: it's going to be tough, let's keep our feet firmly on the ground and prepare for the next matches.
"Our first goal when we saw the group was to go through and that's what we've done."