Argentina suffered defeat in the final of a major tournament for a third straight year after going down to Chile in a penalty shoot-out in New Jersey.
The loss followed defeats in the 2015 Copa final, also against Chile, as well as the 2014 World Cup decider against Germany in Brazil.
Reports suggested Mascherano - just like team-mate Lionel Messi - had retired from internationals, but the Barcelona defender has yet to announce his plans.
The 32-year-old told reporters on Saturday: "With respect to the [Argentina] national team, I will not make any comments.
"It is something I will guard to myself and I prefer not to make any comments to anyone, because we've just finished a very painful Copa America.
"It is not the time to decide anything."
As for his club future, however, Mascherano insists he hopes to continue at Barca for "many years to come", despite reported interest from Juventus.
"I hope that we will have a good season," he added.
"As always, I start the season with a lot of excitement, I hope that it will be the best yet."