Alexis, 29, moved to United in a blockbuster swap deal on Monday which saw Henrikh Mkhitaryan move in the opposite direction to the Gunners.
However, widespread reports on Thursday said Alexis had already travelled to Manchester to seal his switch to United when he was due to be tested at Arsenal's London Colney training complex.
When asked about the responsibility of Alexis missing the test, Wenger said in a press conference on Friday: "On the administration side, it was ours.
“On the day, he had not moved so maybe it was down to us."
Alexis' whereabouts were reportedly unknown to anti-doping authorities as he finalised his move to Jose Mourinho's United, but Wenger is calm about the situation.
He added: “On Monday there was a lot going on. It was a special day for Alexis as you have to do paperwork and travel.
“Negotiations were going on and it's a special event for him to miss a drug test. Overall he's been tested so many times here.
"I'm quite relaxed because we have nothing to hide here and we always try to do our best to cooperate with doping control. I've pushed for football to do more for doping. This was a special day.
"The most important is that the intention is right. The intention of Alexis was not to hide, neither was ours. We have nothing to hide."