The first half at Wembley was cagey as both sides cancelled each other but Arsenal, in particular, were guilty of failing to take advantage of good opportunities.
And the away side were punished five minutes after halftime as Harry Kane towered over Laurent Koscielny to direct a header past Petr Cech and into the Arsenal net.
Spurs had several chances to put the game beyond Arsenal but were wasteful in front of goal.
Alexandre Lacazette could have punished their profligacy in stoppage time but struck his shot wide.
Speaking after the match, Wenger was in no doubt about why his side failed to win.
Wenger said: “The game should have been finished at half-time for me.
“We missed opportunities on the counter-attack that is not acceptable at this level.
“The second half we should have lost the game in the first few minutes, they had lots of chances.
“At the end we should have come back to 1-1.
“Overall it’s mixed feelings, a bit more quality in the first half we could have won the game.”