Valencia's Brazilian-born Spanish forward Rodrigo Moreno (C) celebrates with teammates after scoring a goal during the Spanish League football match between Valencia and Atletico Madrid at the Mestalla Stadium
Gabriel Paulista hit the post for the hosts and Daniel Wass was denied by Atletico keeper Jan Oblak when debutant Michy Batshuayi sent him through on goal in the 90th as Valencia pushed for a late winner but ultimately came up short.
"For much of the game we were superior to Atletico Madrid," said Valencia coach Marcelino. "We had a lot more chances than in either of the games (against them) last season."
Atletico coach Diego Simeone, back on the touchline after suspension forced him to watch the UEFA Super Cup win over Real Madrid from the stands, set up in unusually offensive fashion with no defensive midfielders, two strikers and two wingers.
The visitors started brightly and broke the deadlock when Griezmann's clever pass allowed Correa to beat the offside trap and drill the ball past Neto.
Image credit: Eurosport
However Atletico's more attacking strategy left them open at the back and Spain international Rodrigo equalised with a well-taken goal after Godin misjudged the flight of the ball.
"I scored a good goal after a good move," said Rodrigo. "We played well against an Atletico that give up few chances.
"We showed we are at a high level, this will be what we demand (of ourselves)."
By contrast to Barcelona and Real Madrid's low first game attendances, the Mestalla was nearly full and Valencia fans roared on their team, who nearly took the lead when Gabriel hit the post with a header.
Marcelino threw on new signings Frenchman Kevin Gameiro and Belgian Batshuayi to probe for a winner and Wass should have delivered it but his finish did not have the finesse to beat Oblak.
"There was a lot of disorder in the second half which I did not like," said Simeone.
"Taking points off Valencia is not easy. Last year I said they would fight to improve and I wasn't wrong. This year they will keep growing."