The visitors followed up their 14- try demolition of Gala in the British and Irish Cup at Clifton Park the previous weekend with two tries in either half, including a rare score from hooker Phil Nilsen.
Lowes said: “Our determination in not allowing them to score really pleased me. The two tries conceded are disappointing because they were soft on our part.’
“I thought we moved the ball around well in possession and our defending as a unit is getting better.
“I don’t think we are the finished article yet, and there is certainly more to come from our attack. But it’s a big learning curve.”
The afternoon began badly for the visitors with Ollie Thomas booting the hosts into an early lead after referee Darren Gamage had penalised Leeds at the breakdown.
After a period of attritional play, Leeds won a penalty in the opposition 22 and Glyn Hughes opened his account against his former employers.
Carnegie were penalised for not rolling away and Thomas struck his second penalty.
A well-worked drive from a five-metre lineout resulted in the first try, with long-serving Nilsen touching down after a rolling maul and Hughes converted.
Chris Brightwell charged over for the hosts but hooker Rhys Buckley was sin-binned for instigating a brawl and Hughes scored a try on the verge of half-time.
A fast break from the lively Craig Hampson released the returning David Doherty to open his league try-scoring account for the season after the break.
The fourth try 12 minutes from time secured the win. A grubber kick from Fred Burdon found Jonah Holmes and the Wasps loanee scored his fourth try in as many Championship games.
With Ryan Burrows in the sin-bin for a series of team infringements, a solo try from Alex Day gave Moseley some hope but Leeds safely negotiated the final minutes.
Moseley: Thomas (Owen 44), Armstrong, King, Carter, Williams, Hooley, Brown (Day 62), Warren (Voisey 62), Buckley, B. Evans (Herriott 53), Woolford (Lawrence 62), Powell (Hill 53), Mason (W Evans 34-44), Robinson, Brightwell.
Leeds Carnegie: McColl, Holmes, Lucock, Burdon, D Doherty, Hughes (Lozowski 77), Hampson, Harris (Imiolek 60), Nilsen (Graham 57), Tussac (Beech 63), Smith, Green, Walker, Rowan (Doyle 72), Burrows.
Referee: D Gamage (RFU).