Messi missed a training session on Friday due to the birth of his second son and had also been over in the United States with the Argentine national team.
Messi ultimately came off the bench to secure all three points for the Catalan outfit and Iniesta has insisted that there was no problem in the dressing room.
"He's not angry at being left out. It's normal after the journey and everything that's happened over the last few days. Ultimately, it's the work of everyone that helps the team go forward," Iniesta told reporters.
"Leo is a unique player, he makes a difference and today he did it again. I'm very happy for him and the team.
"We know that games here are always more difficult than normal. We matched the intensity of Atletico when we didn't have the ball and with the ball we played very well. I think we played a very, very complete match."
Barcelona have won all three of their La Liga games in the new campaign.