Goals either side of half-time from Rotherham pair Adam Le Fondre and Stephen Brogan cancelled out Tom Craddock's 19th minute penalty.
But Luton substitute Ed Asafu-Adjaye's equaliser with 16 minutes remaining ensured a replay at Kenilworth Road next week.
It was a patchy display from Rotherham, who had won four consecutive matches in all competitions, and their defensive frailties, which were ruthlessly exposed by Luton, left a sour taste in Moore's mouth ahead of their League Two fixture at Shrewsbury tomorrow.
For Luton's opener, Andy Nicholas scythed down Claude Gnapka in the penalty area when he ought to have stayed on his feet and Gary Roberts took the shine off his bright display by carelessly gifting possession to Luton's Kevin Gallen in the build-up to the leveller.
Rotherham had kept back-to-back clean sheets against Torquay and Lincoln but two lapses in concentration cost Moore's men dearly. They were two soft, inexplicable goals to give away and the Millers will now have to do it the hard way to make the third round.
But give credit where credit is due to non-league Luton, who demonstrated tremendous battling qualities to force a replay and played their part in a thrilling cup tie which had more twists and turns than a rollercoaster ride at Alton Towers.
Moore said: "I just thought we were naive and we gifted them two goals by bad decision-making.
"The penalty was unbelievable and we were naive to get done like that. And for the second they've gone through us like a knife through butter and scored.
"I don't think our goalkeeper has had a save to make. If you play square balls you are always going to be in trouble and it was a silly ball to play.
"They broke three against two and the lad's got lucky as it has gone through Nick Fenton's legs. He couldn't really miss could he?
"But when we went 2-1 up I thought there was only going to be one winner and, for the first time since I've been here, I felt comfortable in the dugout and it was just a matter of when we would get the third.
"But good sides don't concede at 2-1 up. We've got to go on and get three or four but be patient and not go gung-ho and go chasing it. You have to keep the ball and keep the shape and sooner or later they've got to come out and then you pick them off."
Moore had to re-jig his midfield following his team's 2-0 victory over Lincoln and handed Stephen Brogan his first start in 19 months on the left-flank for the injured Kevin Ellison.
New loan signing Adam Rundle was cup-tied after featuring against Luton in the previous round of the competition for parent club Rochdale so Ryan Taylor deputised.
The hosts will be kicking themselves that they did not make their pressure count in the opening 20 minutes when they controlled possession and created a hatful of chances.
Luton were there for the taking and Brogan, twice, and Tom Pope spurned opportunities to break the deadlock.
Cup ties often hinge on the first goal and the match swung the visitors' way after Nicholas was penalised for hauling down Gnapka in the box. It was a stone-wall penalty and Craddock coolly slotted home the spot-kick.
At times, it was difficult to tell who were third in League Two and who were seventh in the Blue Square Premier. The gulf between the two leagues is minimal, and Luton more than held their own after a shaky start.
Craddock's strike knocked the stuffing out of Rotherham and Gnapka almost doubled Luton's lead midway through the first period but he blazed over when well placed.
Rotherham toiled in search of an equaliser and Le Fondre duly grabbed his fifth goal in his last five starts on the stroke of half-time. Taylor freed Tom Pope on the right and his dangerous centre was tapped home by Le Fondre.
The second period was a cagey, scrappy affair, but Rotherham took the lead just after the hour mark when Brogan looped a header over Kevin Pilkington after a pin-point cross from Roberts.
But Roberts turned from hero to villain in the 74th minute when he cheaply conceded possession to Kevin Nicholls and he fed Gallen who slid in Asafu-Adjaye and he lashed his shot beyond Andy Warrington to seal a replay for the visitors.
Luton boss Richard Money said: "It was a good team performance right the way through the side.
"Many people don't expect it to be a shock when Luton draw at Rotherham because we are seen as a big club.
"But you take away the name plates we are a Blue Square Premier club who have avoided defeat to a team in the division above us."



Manager's View
I just thought we were naive and we gifted them two goals by bad decision-making.
The penalty was unbelievable and we were naive to get done like that. And for the second they've gone through us like a knife through butter and scored.

We are disappointed because we have drawn. We are unbeaten in six matches but I am disappointed and the players are disappointed that we have not won the game.

We have got to go do it the hard way. The replay is a game we could do without.

We are looking forward to the challenge at Shrewsbury.

We have won three in a row in the league and we want to make that four.



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