The France forward missed a couple of early chances before collecting two cautions in the first half, for dissent and then tripping Daniel Ivo Pinto.
Dinamo went on to record their first Champions League win since September 1999, having taken the lead against the run of play with an own goal from Alex Oxlade-Chamberlain when the ball bounced back off him past goalkeeper David Ospina, who had saved Josip Pivaric's shot.
The hosts doubled their lead through a powerful header by Junior Fernandes.
Despite a late goal from substitute Theo Walcott, Arsenal were left to reflect on another frustrating European away performance.
Wenger - who had made half a dozen changes with one eye on Saturday's Barclays Premier League trip to Chelsea - pulled few punches in his assessment of the official.
"We were a bit unlucky tonight," the Frenchman said
"I believe the first goal is offside and after the sending-off is very harsh.
"We were not at our best, but nor was the referee tonight.
"The first yellow is Giroud's fault because he protested, even if it was not a foul against him
But after he should not have responded to the referee
"The second yellow card, he is unlucky to touch the guy - he did not see him
It was accidental completely, but it happened
"I don't understand the referee
It has to be on purpose, a foul on purpose
Then the referee should have given many yellows tonight."
Wenger, however, accepted Arsenal were well below the required performance.
"We have for a part to look at ourselves also, because the second goal kills our game
On the corner we were guilty not to defend it well," he said.
"When you don't win the game you have to look at yourself and think you haven't got it right.
"I don't believe the players who came in had a bad game but it didn't work, it didn't work.
"I have to analyse that well
It is very difficult to give a definite answer straight after the game."
Arsenal next host Olympiacos before a double-header with group favourites Bayern Munich.
Wenger said: "Mathematically, we can qualify without any problem if we produce our performances that we want at home.
"Overall, I believe we have problems to start in every competition this season
We had problems in the Premier League and again in the Champions League tonight, but I am confident we can put that right in the next five games."
Dinamo Zagreb manager Zoran Mamic had warned his side had no intentions of giving Arsenal an easy ride at the Maksimir Stadium.
Mamic praised the way Dinamo - who have never qualified for the knockout stages - went about their business.
He said: "I am very happy and proud
I thank the team for doing what I told them and the fans for pushing us when Arsenal had us under pressure.
"Now they have such confidence because see how good they really are.
"After this we are ready for anything which might come, but are also aware of the strength of the group and cannot fall into euphoria."
Source : PA