Argentina – back-to-back runners-up in 2015 and 2016 – were upstaged 2-0 by Colombia in their Copa opener on Saturday.
After a drab first half, Argentina were stunned as Colombia substitutes Roger Martinez and Duvan Zapata condemned La Albiceleste to their first opening-game Copa defeat since 1979.
And Argentina captain Messi – who was largely subdued by Carlos Queiroz's men as he eyes his first senior title with the South American giants – lamented the result.
"We leave here feeling bitter," Messi told reporters afterwards. "In the second half we had our chances.
"It takes time to accept this defeat, but let's see what the next days will be like. We need to look at the horizon and move on.
"We didn't want to start this way, obviously, but now we have to lift our heads and keep going."
"In the first half we retreated a little and were holding on, but in the second we really opened up," said Messi, who almost broke the deadlock in the second half but directed a header just wide of the post.
"Whenever you lose it's hard for us, we usually take it badly. Now we have to think about Paraguay."
Messi continued: "We have to take the positive things of today and think about tomorrow. We have many chances."
Argentina – seeking their first major international title since 1993 – are back in action against Paraguay on Wednesday in Group B.