The French tactician is having to deal with fan discontent on a regular basis and was subject to a chorus of boos from travelling Arsenal supporters when he substituted Giroud for defensive midfielder Francis Coquelin late in the match.
Wenger has also had to juggle Wilshere's workload since his return from an ankle injury.
After playing two games in four days against Tottenham Hotspur and Montpellier, no risks were taken with the 20-year-old on the trip to Villa Park with his ankle being monitored closely for minor inflammation.
"Jack Wilshere has played three or four games in quick succession so I decided to give him a breather on Saturday," Wenger said in his Monday e-mail to Arsenal members.
"It's a relief that he's had no setback since he came back. He had a little inflammation but I think the rest will help him to get rid of it.
"Apart from that, he's done very well. He's not played for 17 months, people forget what that means - it's massive. I'm very happy with the way he progresses."
On his decision to bring off Giroud in the 86th minute, Wenger added: "I took Olivier Giroud off towards the end of the game because he had given everything and was tired. Like Jack, he has played a number of games recently."
With 20 points taken from their first 13 Premier League matches, Arsenal are 10 points shy of leaders Manchester United in sixth.
The North London club are again on the road in their next Premier League fixture when they travel to Goodison Park to face fifth-placed Everton on Wednesday.
Arsenal fans had to deal with the loss of talismanic striker Robin van Persie to Manchester United in August and one ray of light for them this term has been Arsenal's qualification for the Champions League last 16.
