Enterprise was axed in 2005, while later attempts to revive Star Trek for television were rejected by CBS and Paramount.
However, Trinneer, who played Charles 'Trip' Tucker III on the show, told the official Star Trek site that his series was not responsible for the "demise" of the TV franchise.
"I haven't heard anybody who blamed our show for doing that," he argued. "I think that [idea] was nonsense."
Trinneer added that he feels "nothing but pride" for the work performed on Enterprise.
"I think our show, in a sense, got kind of burned," he said. "We happened to be the show [where], for whatever reason, they said, 'Stop'."
A movie version of Star Trek, based on the original '60s series, was released in 2009, with a sequel currently in development.
The film's writers Roberto Orci and Alex Kurtzman recently revealed that they are keen to produce a new animated Star Trek series for television.
Watch the title sequence for Star Trek: Enterprise below: