Colin Calderwood's side lacked the guile and quality in the final third to break down the south Cheshire outfit.
There were few, if any, clear-cut chances and, while Forest had most of the play, home keeper Ben Williams had little to do.
He did make one stunning second-half save from Junior Agogo's 20-yard half-volley.
Crewe handed a debut to loan winger Joe Anyinsah and the Preston youngster arrowed a 30-yarder just past Forest keeper Paul Smith's post in a low-key first 45 minutes.
Sammy Clingan tested Williams with a rising drive and Chris Cohen dragged an abysmal shot past the far post after Agogo had put him in the clear on the left of the box.
Forest upped the game on the re-start with centre-half Wes Morgan in particular forcing himself forward on several occasions.
But the clearest sight of goal they had was when Williams parried an effort into the path of Ian Breckin, but Crewe midfielder Michael O'Connor threw himself across to make a decisive block.
The Alex brought on another loanee, Dean Morgan, with 20 minutes to go and the winger went close with a deflective effort.
But Crewe in the main had to maintain a meticulous rearguard action before they collected an invaluable point.
"A draw away from home is no use to us and with that in mind we knew that we were playing with added pressure," admitted a disappointed Forest boss Colin Calderwood afterwards.
"We have got to try and bridge that gap at the top."