The Robins never looked in danger of conceding against the League Two's bottom club and could even have won the game only to see Chris Senior's 'goal' on the hour disallowed for offside.
Luton started brightly and almost took the lead inside 40 seconds when hesitation from Greg Young in the Altrincham defence allowed Wayne Andrews to latch on to a long ball, but the former Coventry man blazed over from just inside the penalty area.
The non-league outfit settled after that and were almost gifted a goal in the 22nd minute when Keith Keane's badly overhit back-pass caused home goalkeeper Conrad Logan to clear straight to the feet of Senior, but the visiting striker failed to seize on the opening.
Seconds later the Hatters worked an opportunity when Chris Martin hit a left-foot drive just past the post from 20 yards.
The best chance of the half fell to the Robins in the 26th minute when Senior darted in front of Logan to receive a cross and pulled back for Young, who wastefully sidefooted over from 15 yards with the goal gaping.
Altrincham stayed in the ascendancy in the second half and spurned another great chance in the 53rd minute when Colin Little ran clean through only to be denied by Logan.
The visitors had the ball in the net on the hour when Michael Spillane's mistake allowed Little to backheel to Senior who rounded Logan and slid home - only for the effort to be disallowed for offside.
Luton never looked like scoring and the best they could offer was a tame long-range effort from Claude Gnakpa late on that flew harmlessly wide.