Morton were undefeated in their three matches last month and recorded a home win over Partick Thistle to maintain a tilt at the title.
The Cappielow manager picked up his award at Hampden yesterday ahead of tomorrow's Scottish Cup third round tie away to Albion Rovers.
And while Moore was happy to have received recognition, he stressed that the plaudits should rest with his players.
After collecting his award Moore told the Tele: "Without being big headed I got quite a few at Stirling and the good thing about these awards is that they mean the team is doing well.
"That is the only reason we are getting them - it is not because myself or Mark McNally are doing anything different. The players are getting the results on the pitch. I know it is an old cliché but it's true and we've gone on a decent run and played well.
"We are actually being greedy and cursing ourselves about the points we've dropped.
"We thought we should have got the win against Livingston at home at the start of the season.
"The players know that we could be four points better off but we are on a good run.
"Looking at the fixtures coming up, they are winnable games."
One of those games is tomorrow's tie with Albion - the club managed by Moore's former college boss Todd Lumsden.
The gaffer led Ton to a dominant 2-0 home win in the Ramsdens Cup in July but he anticipates a more open contest at Cliftonhill.
He said: "We got them earlier on in the season at home but we are hoping that it might be a wee bit more of an open game this time. They are at home so they might have to come about a bit more - their fans might demand that.
"When we played them before, they were well-drilled but they were never going to beat us. They didn't have any chances.
"But we will be showing them every respect and I will put out the strongest team available as we want to get through to the next round."