Forest will face Yeovil in a fight for a place in the Wembley final, after Bristol City's victory over Rotherham ensured that they earned a place in the Championship ahead of the Reds.
Forest, in fact, finished in fourth place after in-form Blackpool claimed three points at Swansea to overtake them.
And they will need to find more cutting edge if they are to fight their way through to the final, after seeing a succession of chances go begging, as Crewe marked Dario Gradi's last game as Crewe manager with a determined performance.
Forest knew that only victory would be enough to give them a chance of overhauling City and they began with a fitting sense of urgency.
Grant Holt narrowly failed to connect with a teasing Kris Commons cross from the edge of the six-yard box, while Julien Baudet had to clear a Luke Chambers header off the line, as Calderwood's side sought to make an early breakthrough.
David Prutton was guilty of missing the best chance for the Reds, as he found himself in acres of space at the far post, following an Ian Breckin flick-on, but skied his shot wildly over the bar from eight yards.
Ben Williams also made an outstanding save to deny Commons at the near post, as the midfielder looked to add to his tally of five goals in three previous games on the stroke of half-time.
But Crewe too were playing in attack-minded fashion, with the lively duo of Luke Varney and Nicky Maynard often combining to stretch the Forest defence, although both were guilty of lashing shots wide after carving out decent opportunities.
And the party atmosphere had been dampened by half-time, following the news that Bristol City had taken a commanding lead over Rotherham.
After the interval, a Breckin mistake allowed Varney to race clean through on goal, but the Crewe man fired badly wide.
Otherwise, it was again Forest who were largely on top - but they could not make the breakthrough they needed.
Grant Holt headed wide with the goal at his mercy from a Prutton cross and
Jack Lester saw Williams save bravely at his feet after a clever Commons quick free-kick had sent the striker through.
Defender Chambers was twice denied by goal-line clearances from towering headers, while substitute Scott Dobie came even closer, seeing his low shot cannon back off the foot of the post.
But Forest could not make the breakthrough - and will be looking to earn their place in the Championship via the play-offs.