Wenger admitted that the win, which moved Arsenal up to third in the Premier League, had been "fortunate" after a hard fight by Burnley.
"We have been fortunate today to win the game because we were a bit jaded physically and we made some technical mistakes, especially in the first half," Wenger told the BBC, adding that he would have to see the replay of the goal to pass judgement on it.
Just when the home side thought they had secured a hard-earned draw, their defence failed to deal with a short corner that swung in from the right. The ball was headed on to substitute Oxlade-Chamberlain, who bundled the ball on to the hand of a possibly offside Koscielny near the end of added time.
It was a cruel end for Burnley and manager Sean Dyche was predictably unhappy. "You have to question the added time, the corner and whether it should have come in, the handball, and question whether we should have dealt with it," he said.
Burnley had twice gone close to opening the scoring when Sam Vokes headed wide and Michael Keane hit the crossbar.
At the other end, Alexis Sanchez forced a good save from Tom Heaton and blasted wide from inside the area.
With Theo Walcott also missing out with one curled effort, the visitors abandoned their patient approach in search of the winner.
Arsenal are now unbeaten in six Premier League games.
(Reporting by Neil Robinson; Editing by Clare Fallon)
