The actress, who will star in the sequel to the 2009 film, insisted that the reboot has been so successful because of Abrams's ability to make the franchise accessible to everyone.
"[He's] managed to transcend the shackles of the genre," Eve told IGN.
"I think that's what they were probably always striving for. JJ's found a way to make the future accessible to the present.
"He's able to track the story of the heart through this very heightened and stylised, tactical universe."
Benedict Cumberbatch has also joined the sequel. Chris Pine recently praised the Sherlock star's performance, describing him as "super talented".
The Star Trek sequel will be released on May 17, 2013.
Watch the trailer for Alice Eve's upcoming movie Men in Black 3 below: