Messi, mesmerising for Barcelona, has had limited influence in the hosts' first two matches in Group A, a 1-1 draw with Bolivia and Wednesday's 0-0 stalemate with Colombia.
Coach Sergio Batista preaches a game that is centred around Messi but it is not working in a competitive context in the way it appeared to flourish in friendlies.
Argentina have been thwarted by two well organised sides with Colombia's Hernan Dario Gomez showing the extent of his nous as a coach in his near-flawless tactics against Batista's.
Had Colombia's attack put away one of several chances, the game plan would have been perfect but they were profligate while Argentina's Sergio Romero had a man-of-the-match game in goal.
The best thing Messi did in the 90 minutes against Colombia was the brilliant through-ball to Ezequiel Lavezzi in the first half that the winger should have buried in the Colombia net.
That is not, however, the role Batista really has for Messi. He wants to see Messi receiving such passes and putting away the goals himself.
It will hardly ever happen while Batista plays three natural central midfielders in Javier Mascherano, Ever Banega and Esteban Cambiasso and no true link-man like Juan Roman Riquelme.
Riquelme and Messi combined to inspire Argentina to Olympic gold in Beijing in 2008, the one international title Batista has won as a coach.
There is a classic playmaker in Argentina's Copa America squad, Javier Pastore, but Batista seems reluctant to use him even as a substitute.
"I remain confident in these players, I have the players (but) the functioning (of the team) is costing us a bit," Batista told the post-match news conference.
"One tries to give them a footballing idea, but in these two matches we haven't seen it."
Batista said he would stick to his guns, adding: "We're going to continue to try playing good football, we're not going to try to win any old how."
Colombia's performance, in contrast, was pleasing for Gomez, who said: "We had a decent match and I think we're building something important for the 2014 (World Cup) qualifiers.
"There are things we do in training and it's gratifying for one to see them in matches, above all against rivals that are as capable, strong and at home as Argentina, with the class of players they have."
Whatever Batista and his troops practise behind closed doors is not appearing on the pitch -- which they left to boos and whistles from Argentina fans.