Mick Harford's side - still stuck on zero in League Two after starting the season with a 30-point deduction - battled gamely throughout against League One strugglers Brighton.
Recalled Seagulls striker Jake Robinson failed to connect from a good position early on and also forced Luton goalkeeper Conrad Logan to parry his shot shortly after the break.
Brighton lacked quality in the final third and Robinson should have put them ahead after only 13 minutes but failed to connect from the edge of the six-yard box. He could not capitalise after Kevin McLeod's whipped cross just eluded skipper Nicky Forster.
Luton keeper Logan came to his side's rescue shortly after the break as he parried a goalbound strike from Robinson.
Seagulls midfielder Adam Virgo, unmarked at the far post, headed wastefully over after Tommy Fraser delivered an accurate cross. Luton rarely threatened in front of goal, although Asa Hall directed a header wide at the far post following Rossi Jarvis' free-kick 14 minutes from time.