"I am not the person to discuss a decision of Federation Internationale de Football Association, but it seems an outrage to me that they have given Messi four matches", Pique said.
"It is impossible to replace Messi, " said Cesar Luis Menotti, Argentina's World Cup winning coach in 1978. Without its star striker, Argentina fell, 2-0.
He was also fined 10,000 Swiss francs (9,350 euros, $10,170).
The suspension does not apply to games for his club, Barcelona.
Argentina has announced plans to appeal the decision, voicing particular outrage at the timing of the announcement, falling days after the Chile game and only hours before the match in Bolivia. "We feel powerless, surprised".
Argentina is now in the fifth place.
The 29-year-old Messi will also miss Argentina's games away to Uruguay and home to Venezuela and Peru.
He was caught on camera venting his fury at an assistant who signalled he had committed a foul late on in Argentina's 1-0 win. He waved his arms and shouted profane insults at him. No further action was taken at the time.
Messi avoided any kind of sanction during the game, but he didn't settle down and refused to shake Van Gasse's hand at the final whistle.
Neymar had a chance to make it 2-0 in the 53rd minute from the penalty spot only to see his kick saved by Anthony Silva.
Messi has not enjoyed the same success with Argentina as he has with Barcelona and announced his worldwide retirement past year before back-tracking on his decision. It seems like Argentina's only hope is to have the suspension reduced.
Messi is one of five players suspended for the visit to Bolivia after Nicolas Otamendi, Javier Mascherano, Lucas Biglia and Gonzalo Higuain picked up yellow cards against Chile. The team was the runner-up in the 2014 World Cup and the Copa Amrica in 2015 and 2016.
The 29-year-old will also miss Argentina's game at Uruguay on August 31, and home games against Venezuela on September 5 and Peru on October 5.