Diego Simeone's men had a number of chances to score an important away goal in the first leg of the round of 16 tie, but they eventually failed to break the deadlock as Luciano Vietto and Griezmann missed big chances, while Diego Godin saw a goal disallowed.
PSV were reduced to 10 men halfway through the second half following Gaston Pereiro's dismissal, but eventually held on to record a valuable draw, much to the frustration of Griezmann.
"It's annoying to just draw when you want to win," the France international told the official Uefa website.
"It wasn’t easy; it was a difficult game. We worked hard at the back and then the chance I got was a shame. I didn't get my body shape quite right and the goalkeeper did well. But it doesn't matter. I'm still full of confidence.
"When they went down to 10 players, it was perhaps more difficult because they closed shop at the back.
"It's not so bad. We're at home next time and it's a boost. At home we’re comfortable with our fans who push us on in all we do and I’m sure we’ll do well."