The Gunners signed the Ghana international after activating his £45million (€50m) release clause during the final hours of the transfer window.
Atletico, who then brought in Arsenal's Lucas Torreira on loan, were reportedly upset with the way the fee for Thomas was deposited at close to midnight Spanish time and that the player was prepared to quit the club in such prompt fashion after eight years.
Simeone has seen stars including Rodri, Lucas Hernandez and Antoine Griezmann depart in recent years after their buy-out clauses were met and he insists he holds no grudges against the players themselves, even if the manner of the exits is something the club can do little to prevent.
"I keep thinking Lucas' exit was very important," Simeone told reporters on Friday. "He was a boy from the academy, with a lot of strength and a future, as we see with his national team, but we can't give many opinions against situations involving these clauses.
"Everything that happens to the boys who gave me a lot of things at the club makes me happy. Thomas is a boy I remember from when he played in the B team with Saul [Niguez].
"We started to bring him up, it took a lot out of him, he went to Almeria and it was difficult for him to find stability in the club.
"He's an incredible player and we wish him the best."
Simeone hopes to see Torreira make a significant impact, saying: "I'm not going to talk about what we win or lose with Thomas because he's not here. What Lucas will be able to bring to the team is vitality, dynamism in the middle.
"He comes from a time when he was not playing and he does so with great excitement."
Atleti started the LaLiga season with a 6-1 victory over Granada but have followed that result with back-to-back goalless draws with Huesca and Villarreal.
Simeone has hinted he could start Luis Suarez, Diego Costa and Joao Felix together in a bid to get his side's attack firing again and says Portuguese forward Felix must endeavour to bring his international form to club level.
"Of course they can play together. Many of the players we have can play together. We'll see at what moment, what situation and in what state each one is," Simeone said.
"He [Felix] is a very important player for us. I saw the games he played with the national team and I liked his work.
"He has talent and he can appear at any moment, but what I saw with Portugal, where he showed commitment, intention, enthusiasm for what the team needed - that speaks highly of him and it's what we also need from him."