The 24-year-old believes the former Barcelona star will more than compensate for the loss of the Colombian this season.
The Colombian hit 70 goals in total throughout his two-year stay in the Spanish capital prior to his 60 millioneuro move to Monaco, prompting the Rojiblancos to swoop for Barcelona striker Villa earlier this summer.
Costa is convinced the Spain international will prove a more than adequate replacement for the 27-year-old Falcao, describing him as a "beast" who gives his all for the side.
"You notice the absence of Falcao because he is a great player, but we have Villa who is also a beast and we know that he is going to do just as well," Costa told the club's website.
"His work and commitment for the team is amazing. He is a very humble person and he has a great attitude. I think with the quality he has he will give a lot to Atletico."
Villa, 31, will face former employer Barcelona for the first time since his summer move when Atleti hosts the Liga champion for the first leg of the Spanish Super Cup on Wednesday.