Alexis Sanchez scored a 92nd-minute winner from the spot after Aaron Ramsey was adjudged to have been pushed over in the area by James Tarkowski.
Burnley were incensed by the decision, which consigned them to a third-successive stoppage-time defeat against the Gunners - the last two of which have been sealed by Sanchez spot-kicks.
However, Wenger was strong in his initial assessment of the incident.
"It looked a clear penalty. I will have to watch it again. I can understand [Burnley] are disappointed," Wenger said at his post-match press conference.
"[Ramsey] didn't throw himself on the ground. He said he wanted to flick the ball on and was pushed on the back."
Arsenal had appeared set to drop points on the road for the sixth time this Premier League season, having struggled to create chances in the absence of Mesut Ozil, who was ruled out through illness.
But an improved display after the interval resulted in what Wenger felt was a warranted second away win of the campaign.
"After the win against Tottenham, it was important to go away and win and that's what we did," he said.
"In the second half, I felt was all us... even if we missed our final ball.
"We kept a clean sheet, we won 1-0 and I want to congratulate my three centre-backs [Nacho Monreal, Laurent Koscielny and Shkodran Mustafi]."