The comedy drama - based on the Douglas Adams novels - began with a pilot episode in 2010, with three hour-long episodes following in March this year.
However, Mangan - who played the title role - revealed on Twitter that the show will not return to BBC Four.
He wrote: "It gives me no pleasure whatsoever to report that the BBC have decided not to make any more Dirk Gently."
The Dirk Gently pilot episode attracted 1.1m in December 2010, but the third and final episode saw just 592,000 viewers tune in.
Darren Boyd, Helen Baxendale, Jason Watkins and Lisa Jackson also appeared in the series alongside Mangan, while Howard Overman (Misfits) adapted Adams's books for television.
In 2011, Mangan admitted that he would be "heartbroken" if BBC Four ever cancelled Dirk Gently.
"If they axe [the series], I'll go round there and smash the place up with my bare hands," he joked.
