Wenger tried to push Taylor out of the way when the official went to tell him that he was not allowed to watch from the corridor of the tunnel.
If Arsenal are to win the title for the first time since 2004, they will need focused performances from Alexis Sanchez and Mesut Ozil, but Wenger has so far offered no updates on the apparent impasse over the duo's proposed new contracts.
"I regret everything and I should have shut up", Wenger joked. Football has become a bit like that as regards managers, so I think it is unlikely that you will last that long, and the ones that do last that long will do so because they have a lot of success.
Asked to explain why he had been sent off, Wenger added: "Myself?" I apologise for that.
Burnley had fought back after Shkodran Mustafi's first-half opener, equalising though Andre Gran's penalty in the 93rd minute, following the sending off of Granit Xhaka on 65 minutes.
As well as the missed Koscielny offside, there was yet another red card for Granit Xhaka, his fourth of the season, for a scissors tackle on Burnley's Steven Defour. The Switzerland worldwide lunged into a challenge with Burnley's Steven Defour.
"Overall I believe that made the game much more hard for us, nervously and physically".
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And Burnley appeared on course for just a second away point of the season when Gray converted a late penalty, only for more drama to follow.
"I didn't know if I was sent to the stand but I was sent out".
"He was too cool [with the penalty]", assessed Wenger. In the 50th minute Sanchez again fizzed an effort just over after picking the ball up on the right.
Burnley came back strong and equalised in the 93 minute.
It was the Switzerland international's second red card of the season, having also been sent off by Moss in a 3-2 home win over Swansea City in October, which means he gets an additional game on top of the standard three-game ban.
Arsenal's Laurent Koscielny is fouled by Burnley's Ben Mee in the area resulting in a penalty to Arsenal.
"As long as you can not take your chances you're always susceptible to concede a goal against them because they are quite efficient".