The result leaves both teams fighting against relegation, but Blackwell was keen to acknowledge the efforts of his players.
"I am delighted with the players, their application and work-rate, particularly in the second half was excellent," he said.
The result means that Burnley have now gone 18 league games without a win and left boss Steve Cotterill to reflect on another disappointing scoreline.
Luton suffered an early blow when influential central defender Leon Barnett was forced to leave the field with a torn hamstring.
Burnley's best opportunities came in the first half and fell to leading scorer Andy Gray.
A header from Gray brought a fine save from Dean Brill and the Luton keeper was again in action shortly afterwards to deny Gray for a second time.
Luton began the second half much more brightly and created an opportunity after fine play down the right by Matthew Spring, whose cross was headed over at the near post by Dean Morgan.
Morgan then shot into the side-netting after collecting a throw-in from full-back Sol Davis.
Spring should have done better than tamely shooting at Clarets keeper Brian Jensen from the edge of the box.
With Luton dominating the second period, Steve Cotterill made a double substitution with Kyle Lafferty and James O'Connor replacing Ade Akinbiyi and Steve Jones.
Not to be out-done, Luton boss Kevin Blackwell responded with a double substitution of his own as Kevin Foley and Calvin Andrew replaced Davis and Morgan.
With time fast running out, Brill was called upon to make a rare save from a Wayne Thomas strike.
However, despite the numerous half-chances, this game was always heading for the inevitable goalless draw.