Messi, 32, has faced criticism for his performances for the national team as his wait for a first senior trophy at international level goes on.
But Ajax defender Tagliafico, a 25-time Argentina international, said the Barcelona star was key for his nation.
"Messi was released from the pressure to get results [at the 2019 Copa America, where Argentina finished third]," he told Ole.
"He more than anyone gets angry when he loses, but Messi became more aware that he has to enjoy the national team.
"I don't know until when he will play, but it is not that he will have too many cups with the national team. He is at a stage where he wants to enjoy everything, training, games.
"He is the leader and protector of the team. That facet came out that we might not always see."
— Selección Argentina (@Argentina) March 27, 2020
The Copa America was due to be played again this year, but has been pushed back to 2021 due to the coronavirus pandemic.
Tagliafico said it was crucial for Argentina, who are unbeaten in seven games, to develop a strong foundation.
"We must find a very solid structure, not only for Leo, but also for the future, for what is to come," he said.
"To be able to find a structure to grow. It is good to build a solid foundation and don't build a base and then take it apart.
"If we can help Leo and Leo can help us, we will do much better. Everything is going to multiply. You have to create a structure and from there start to grow."
Photo Getty Images Caption: Lionel Messi in action for Argentina