Argentina captain Messi levelled in the 57th minute after a handball by Paraguay's Ivan Peris which no one on the pitch appealed for but was spotted by a VAR review.
But Argentina also had goalkeeper Franco Armani - perhaps lucky to still be on the field at that point after denying Derlis Gonzalez a clear goalscoring opportunity in the first half - to thank for saving a second-half penalty.
Following their opening-game defeat to Colombia, Argentina lie bottom of Copa America Group B. The Colombians secured top spot ealier on Wednesday by beating Qatar 1-0 thanks to a late Duvan Zapata goal.
Colombia leads the group with six points, four more than second-place Paraguay and five more than both Qatar and Argentina.
Do you think they can progress in the Copa America?
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The forward admitted he could have continued if Scaloni had not replaced him with Angel Di Maria. Messi and Sergio Aguero are likely to play with Lautaro Martinez or Paulo Dybala, who has played zero minutes at the Copa America.
The 25-year-old speed machine can play as a winger or in the number 10 role and he's already a big favourite at St James' Park.
'Frankly, it's a little frustrating not being able to get the win we need to take the next step, ' Messi told reporters following the 1-1 draw against Paraguay. Argentina vs Paraguay football match will be held on June 20, 2019, as per India time at 6:00am IST (Indian Standard Time) 9:30 pm BRT, 8:30 pm ET Estádio Governador Magalhães Pinto. "It will take some time to accept this defeat, but we have to take the positives from today and move on to try to win the next match".
This is a crucial game for Argentina and one they must win.
- Argentina have earned only one point in their first two matches of the tournament, their worst Copa America start since 1979, when they lost their first two games.
"Our best player was the entire team", Colombia coach Carlos Queiroz said.