Partey, 27, joined the Premier League club on Monday night after they paid his €50 million buyout clause.
Atletico said they were informed by La Liga at 11.28 p.m. Spanish time -- just over half an hour before the transfer window closed -- that Arsenal's representatives had been at their Madrid headquarters that evening to exercise the player's release clause.
Sources told ESPN that Atletico were "resigned" to Arsenal's actions rather than being upset by them.
The club had been aware there could be some late movement in the market, and coach Diego Simeone admitted on Saturday that the club were "worried" about "bad surprises, which can always happen in football," ahead of deadline day.
ESPN reported in August that Atletico were concerned about having to replace, or cope without, one of their biggest stars -- such as midfielder Partey or goalkeeper Jan Oblak -- if a club paid their buyout clause this summer.
That led to an air of acceptance at the club's offices on Monday when the news broke, and a realisation that there was nothing they could do about it.
The difference in Partey's case is that the departure came in the final minutes of the window, although Spanish rules give them an extra month to find a replacement, as long as that player comes from within La Liga.
Nonetheless Atletico were unimpressed with Partey's willingness to leave a club where he'd spent eight years -- being viewed as akin to an academy product after joining as a teenager in 2012 -- in this manner, putting them in a difficult position.
Partey broke into the first team in 2015, and became a key player over the past three seasons, but remained one of the worst-paid members of the first-team squad, despite being among the best performers.
The club had offered Partey a new improved contract earlier this year before the coronavirus pandemic, which he rejected.
He was later offered a reduced deal in the new financial environment, with Atletico desperate to increase his buyout clause to a figure more reflective of his market value.
That offer was ignored and Partey went on to be linked to Arsenal throughout the summer.
Atletico maintained that no formal bids had been made, with the Gunners reluctant to pay the full value of his clause and Atletico refusing to negotiate, until Monday's dramatic late-night conclusion.
Later on Tuesday, Atletico full-back Kieran Trippier tipped his former teammate to adapt quickly to the Premier League.
"He's unbelievable, his physicality, how he breaks up play. Technically he's got everything. He ranks as one of the best midfielders I've played with," he said. "He speaks perfect English. I don't think he'd have a problem with the Premier League."