The Rojiblancos left the Basque Country with all three points thanks to goals from Saul Niguez and France international Griezmann in the second half of the match.
It was a classic Atletico performance in the way they were able to grind out the victory, which Griezmann hopes will stand his side in good stead as they attempt to cut down rivals Real Madrid's nine-point lead at the top of the table.
"We are playing like Atletico again - defending well and not conceding, while we try to make something out of the few chances we have up front," Marca quotes him as saying.
"It was a difficult match at a difficult stadium, but we gave everything. We found it tougher in the first half, before we improved in the second."
Griezmann, heavily linked with a summer switch to Manchester United, ended a run of 822 La Liga minutes without a goal with his strike against Eibar.