Second-half goals from Marek Tomana, Colin Cramb and Dene Shields put Stirling on easy street against a Forfar side who had Gavin Beith sent off on 72 minutes for his second booking as they crashed to a fifth straight loss.
Moore said: "We looked as if we were fitter than them and that told in the end but it was disappointing not to score more goals.
"Goalscoring becomes a habit but we missed some glaring chances. Colin Cramb could have had a hat-trick but at least he scored one to shut me up because I had been nipping his head for the misses!"
Loons keeper Sean Murdoch allowed Tomana's free-kick to slither under his body for the 48th minute opener then Cramb weaved his way into the area and scored with a low shot after 64 minutes before he set up substitute Shields to head the third in injury time.
Forfar boss George Shaw moaned: "The second-half performance wasn't good enough and our heads went down after we lost the first goal.
"With the exception of Alan Rattray the defending was shocking and if I had another centre-half and full-back to bring in then I would."