Boro blew the title race wide open with their first win in 12 games, the victory lifting them out of the bottom three.
An early penalty from Stewart Downing and a second goal in a week for Tuncay Sanli handed the home side a richly-deserved three points, with Tomas Rosicky netting a stoppage-time consolation for the visitors.
It capped a north-east double-whammy for Arsenal, who were held 1-1 at Newcastle in midweek and now lead the table by only a point from champions Manchester United having played the same number of games.
"We lost the game because we deserved to lose it," said a magnanimous Wenger.
"It's that simple. Middlesbrough were sharper in the fight.
"We missed the start of the game by giving them too much room and it cost a penalty.
"From then on, it was down to us being a little bit jaded physically.
"It was our fourth away trip on the trot.
"We gave absolutely everything to come back. We lacked creativity, sharpness in our passing so therefore we were not dangerous enough to come back into the game."
Wenger said he would watch the penalty award again before deciding whether it was correct.
It looked like a good call from Howard Webb after Kolo Toure's clumsy challenge felled former Gunners team-mate Jeremie Aliadiere.
"It gave them a lot of courage," Wenger said of the incident.
"In fairness, they defended well, Credit to them, they were sharper than us and you could see, once we were 1-0 down, if we do not come back before half-time, it will be difficult."