Costa, who earned a recall to La Roja following his impressive form at Atletico Madrid since January, feels a player like the FC Barcelona record-scorer should be celebrated by La Albiceleste fans and not criticised for not securing silverware for the South American nation.
The 30-year-old has scored 61 goals in 123 games for Jorge Sampaoli's side but has been the scapegoat for their recent failures in the Copa America and 2014 World Cup final defeat to Germany.
Costa pin-pointed the result in Madrid this week as a key reference to Argentina without their influential captain on the field of play.
"You need to do an analysis of all areas, in Argentina, you criticise Messi a lot but when he is not playing then it is a different story," said Costa, as quoted by AS.
"You shouldn't criticise a player like Messi but thank God that he is there. Messi should be treated well always whether or not he played badly because he can make the difference."