Nigel Pearson could barely contain his frustration after a late Dan Bentley error extended Bristol City's run without a home win to 14 games.
The Robins grabbed the lead against the run of play when Nathan Baker headed home Jay Dasilva's 57th-minute free-kick.
But, with the game in stoppage time, goalkeeper Bentley failed to gather the ball at the feet of Carlos Mendes-Gomes, who crossed from the left for substitute Danny Hylton to tap into an unguarded net.
Pearson said: "Dan made some fine saves in the game, but will be disappointed with that moment.
"I didn't say anything to him after the game because that is not the right time. But the fact is that an individual error has cost us.
"I am as frustrated as everyone else by our struggle to win here. But I have to contain my emotions and take time to assess the performance.
"We were not at our best. Luton outplayed us at times and we could have been two or three down at half-time.
"But we then got ourselves into a position to win the game and should have seen it out.
"The team are fitter than last season and I have great faith in this group of players. I want to be positive, but I feel for our fans and we have to find a way to end this run."
Hylton's goal meant City have still not won at Ashton Gate since January – 11 of the 14 games under Pearson's management.
Luton boss Nathan Jones was dissatisfied for a different reason, and said: "I am not happy with a point in the least because we should have been out of sight by the break.
"The chances we created were really good ones and I'm disappointed we didn't take one or two of them.
"But my team again showed tremendous character and kept going to the very end.
"I always describe the players on the bench as gamechangers, rather than substitutes, and we have seen the ones I sent on tonight justify that description.
"We had to set the tempo of the game because Bristol City were breaking it up at every opportunity, taking time to wipe the ball at throw-ins and in other ways.
"I thought we did that really well and the only thing missing from our first-half display was goals."
Jones was forced into a late change when skipper Sonny Bradley suffered a recurrence of an injury in the warm-up and was replaced by Kal Naismith.
"It's not the first time that sort of thing has happened recently," said Jones. "But again we readjusted and came up with a performance."
