After a goalless game, the Albiceleste were edged out in the second half of extra-time by Mario Gotze's 113th minute winner and the trophy was won by Joachim Low's side.
"I think we played really well and we deserved a bit more," Messi told reporters after the game. "We were so close to penalties and penalties would have been another story.
"We had our chances. They had more of the ball, but we had the clearest chances."
The Argentina captain, who was given the Golden Ball award for the tournament's best player after the game in Rio de Janeiro, missed one his side's best openings as he dragged a left-footed shot wide of the target in the second half.
"It didn't go in and we have to move on," he said. "I wanted to lift the cup for Argentina and for the people, but it wasn't to be and we're very sad."