The result may even lead to the end of McMenemy's reign. The former Southampton manager's contract with Northern Ireland expires at the end of this qualifying campaign.
McMenemy had gambled on the untested Bournemouth striker Stephen Robinson for what was his most important match since taking charge. But the move failed as the 24-year-old Robinson struggled to bridge the gulf in quality between the Second Division and international football.
He could make little impact on the match, apart from getting in the way of a Keith Gillespie effort in the first half. In truth the Irish generally created very little, although Iain Dowie appealed in vain for a header which he felt had crossed the line.
McMenemy had told his captain, Steve Lomas, to push forward at every opportunity in support of Robinson and Dowie, and he went close with a 25-yard shot early on.
Gillespie also tried his luck from the right only for his effort to cannon off Robinson. Michael Hughes made his mark on the game and Oleg Fistican's legs on 13 minutes when he chopped down the Moldovan to earn a yellow card.
Moldova, whose last competitive win was almost four years ago, rallied and Igor Oprea's cross from the left was headed over by Alexander Sukharev.
That effort brought the home fans to life, although Northern Ireland's small travelling band of supporters were also making themselves heard.
Maik Taylor proved he was not suffering any after effects from Saturday's 3-0 defeat against Germany with a fine save from Sergiu Epureanu's 20- yard free-kick. Then just before the interval, Vladimir Gaidamaschuk raced clear, only for Darren Patterson to bring him down.
There was little to pierce the gloom after the break, the game plunging to new depths of tedium and the Moldovan crowd presumably wondering if the entertainment on offer was really worth a day's wages.
Kevin Horlock became the third Irish player to be booked in the 61st minute before Aaron Hughes came on for Patterson two minutes later.
Midway through the half came the moment when Dowie felt he had scored. The veteran striker got his head to Lomas's long throw-in, but the Croatian referee ruled that Sergei Dinov had palmed the ball away before it could cross the line. With that decision went any lingering Irish hopes of qualification.
MOLDOVA: Dinov (Constructorul Chisinau), Fistican (Zimbru Chisinau), Rebeja (Uralan Elista), Sosnovsky (Dynamo Kiev), Guzun (Torpedo Zaporizhya), Stroenko (Tiligul Tiraspol), Sukharev (Dnipro Dnipropetrovsk), Oprea (Zimbru Chisinau), Gaidamaschuk (Sherif Tiraspol), Epureanu (Zimbru Chisinau), Kleschenko (Zimbru Chisinau). Substitute: Stratulat (Nistru Otaci) for Oprea, 90.
NORTHERN IRELAND (4-4-2): Taylor (Fulham); Patterson (Dundee United), Horlock (Manchester City), Williams (Chesterfield), Morrow (Queen's Park Rangers); Lomas (West Ham), Gillespie (Blackburn Rovers), Lennon (Leicester City), M Hughes (Wimbledon); Dowie (Queen's Park Rangers), Robinson (Bournemouth). Substitute: A Hughes (Newcastle United) for Patterson, 56.
Referee: E Trivcovic (Croatia).