Argentina's progress to Tuesday's match has largely been inspired by Messi, the forward scoring four and assisting two of their nine goals.
"He has always been like this," said Lyon left-back Tagliafico.
"For us he is our captain and our leader. He is the one pushing us and motivating us."
Messi will equal Germany great Lothar Matthaus' 25-match tournament appearance record against the 2018 World Cup finalists at Lusail Stadium (19:00 GMT).
The 35-year-old also has other personal milestones in view as he looks to lead Argentina to a first triumph since 1986, in his fifth and likely last World Cup.
As well as being Argentina's joint-highest goalscorer alongside Gabriel Batistuta in the competition with 10, Messi is one assist away from equalling Diego Maradona's overall record of eight at World Cup finals.
"He is the one who gives us that special advantage when we are on the pitch," added Tagliafico.
"We know we have Messi and it is a great source of motivation and hope because we all know that we can contribute and give our best. We are really happy to have Messi as our captain.
"With everyone's support we are all working together to achieve our dreams, and it is the most beautiful thing to do it with Messi by our side."
With a population of less than four million, Croatia head coach Zlatko Dalic says advancing past Argentina to reach a second successive World Cup final would have to be considered his nation's greatest footballing achievement.
Victory for Croatia on Tuesday would also see them become only the second side after Germany in 2014 to eliminate both Brazil and Argentina in the knockout stages of the same World Cup.
"The semi-final match against England in the last World Cup [in 2018] was the greatest match of all time, the game against Brazil comes in second," Dalic said.
"If we win tomorrow that would make it the greatest historical game for Croatia of all time.
"We are among the four best teams in the world - that is an extraordinary success for Croatia. It is a great thing for two World Cups in a row to be in the four best national teams in football.
"We want more. We are playing the great Argentina, a terrific team led by Lionel Messi. They are highly motivated and under more pressure than Croatia at this moment in time."
Meanwhile, Argentina boss Lionel Scaloni has defended his players over accusations of misconduct and poor sportsmanship following their bad-tempered penalty shootout win over the Netherlands in the quarter-finals.
Argentina players mocked their Dutch opponents at the end of the match and Fifa subsequently opened disciplinary proceedings against both sides after the encounter saw a World Cup record of 18 yellow cards issued.
"The previous game was played the way we had to play - for both teams. That's football," Scaloni said.
"In some games things can happen like this. There can be arguments but that's all. That's why there's a referee.
"We need to put an end to this idea of thinking Argentina behave like this. We lost to Saudi Arabia and we didn't say anything.
"We won the Copa America in Brazil and experienced the most sporting behaviour with [Lionel] Messi, [Leandro] Paredes, Neymar, who were all sitting together in the tunnel in the Maracana [Stadium]. I'm really not convinced of this idea of unsporting behaviour."
Argentina will be without the suspended Marcos Acuna and Gonzalo Montiel, with Tagliafico set to come in at left-back.
However, both Angel di Maria and Rodrigo de Paul will be fit to play for Scaloni's side.
Croatia boss Dalic has no injury or suspension concerns and will be able to select from a fully fit squad after Borna Sosa and Mislav Orsic recovered from illness.
-- Courtesy of BBC Sport