The great rivals, who hold a joint record of 14 titles in South America's elite tournament, clash in another "Clasico del Rio de la Plata" in Santa Fe on Saturday with both looking to improve on their performances to date.
Argentina came good in their last Group A match when they beat Costa Rica 3-0. Messi was close to his creative best but is still without a goal for his country in 15 competitive matches.
"If you have a problem and you don't have the solution, why worry? Messi can give us a lot of problems which won't go away whatever we do to try to avoid them," Tabarez told reporters in Buenos Aires.
"But there are a lot of things we can do that neither Messi nor anyone else can prevent, those things that are part of the identity of this squad, of being stubborn, of believing we can [do it]," he said.
Diego Forlan, voted player of the 2010 World Cup where Uruguay were surprise semi-finalists, has also yet to find the net and his partnership with Luis Suarez has suffered without the presence of injured Edinson Cavani, the third man in the side's attacking triumvirate.
This does not make Messi, who will play a remarkable 66th match this season, any less wary of the potential Uruguay have to spoil Argentine ambitions of ending an 18-year wait for a major title on home soil.
"Forlan is a great player and we all know we can't give him any room [because] he kicks well with both feet [and] links well with Suarez," Messi told reporters at Argentina's base camp outside Buenos Aires.
"Playing against South American national teams is very difficult, they play with two lines of four... we have to find a way round that," he added, having struggled with the marking in Argentina's draws against Bolivia and Colombia.
Dark horses Colombia and Peru play in the second quarter-final on Saturday. Neither team has enjoyed much success in recent years.
Peru last reached the World Cup finals in 1982 and finished bottom of South America's 2010 qualifiers.
Colombia have fared a little better and were the last team to deny Brazil the Copa America trophy in their only title as hosts in 2001. They now appear to have the potential to rival their great 1990s generation, however.
"This [team's] football is quicker than in those days, because of the players' characteristics but they too have good technique and tactical discipline," said coach Hernan Dario Gomez, the link with the sides that went to three World Cups between 1990 and 1998.
A win for Colombia on Saturday would bring a re-match with Argentina following their stirring 0-0 draw in the group phase.
Champions Brazil face Paraguay in La Plata on Sunday before Chile and Venezuela clash in the last of the quarter-finals in San Juan.
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