Wenger, who has so far failed to land any major summer transfer targets, saw his side racing into an early lead through Olivier Giroud.
However, Villa - who spent much of last season battling against relegation - hit back when Christian Benteke equalised from a penalty rebound.
In what proved to be the defining moment of the match, the visitors were awarded a controversial penalty on the hour when Laurent Koscielny looked to have won the ball in his challenge with Gabriel Agbonlahor, before Benteke netted from the spot.
The France defender, booked for his challenge, was then soon shown a second yellow by Taylor for clattering into Andreas Weimann
Arsenal - who face a crucial Champions League play-off first leg away to Fenerbahce on Wednesday - rallied with 10 men, but were not able to break down a determined Villa defence, as goalkeeper Brad Guzan made a couple of smart saves.
New signing Antonio Luna added a late third for the visitors - before unhappy chants of ''spend some money'' rang out from the home support at full-time.
Wenger, though, was left perplexed by the whole series of events in a match which was also notable for featuring the first use of the Premier League's new goal decision system (GDS) when a 52nd-minute effort from Villa midfielder Fabian Delph struck the inside of the right-hand post and rolled across the line.
"I didn't like his performance, but more than his performance I didn't like his spirit of how he refereed the game," Wenger said of Taylor. "I didn't like the fact the way the game was refereed and this is a deeper question that just one decision.
"I don't like to lie, I didn't like what he did.
Source: PA
Source: PA