Garcia has been named the Sky Bet Championship Manager of the Month for November, with McCormack winning the player award.
Garcia's Brighton went the entire month unbeaten, winning three and drawing one of their four matches, including a 3-0 win over Blackburn Rovers.
"I would like to dedicate the award to the fans, who have been so supportive since my first day at Brighton & Hove Albion, fill the stadium for every match and support us away from home," said Garcia.
"I'm very proud to receive the award on behalf of the club, and proud of the players and staff because they are the ones who deserve the award.
"This is an award for everyone, it's not an individual award, as it is ultimately the team's results in November which won the award.
"We have shown what we can do, with a great month of results and performances, the challenge now is to continue that going forward."
Former Charlton Athletic manager Alan Curbishley chairs the Sky Bet Manager of the Month judging panel and said: "Oscar is now making an impact at Brighton following his appointment over the summer.
"He fully deserves this award and will be hoping to extend Brighton's form as we approach the busy festive period."
Sky Sports' Football League pundit Don Goodman said: "Three victories took Brighton from 16th to ninth in the Sky Bet Championship in November.
"After a difficult October, Oscar has tightened the defence and got his team scoring much-needed goals."
Leeds striker McCormack has been named the Sky Bet Championship Player of the Month after scoring seven goals in November, including all four in the 4-2 win away to Charlton.
Leeds United manager Brian McDermott said: "I'm delighted for Ross winning Player of the Month, quite rightly in my opinion, although I'm biased!
"He has started December well with two goals, and let's hope he can win it this month as well."
Brentford's Uwe Rosler has been named the Sky Bet League One Manager of the Month after his Bees went five games unbeaten, including an emphatic 5-0 win against Crewe Alexandra, extending their run to eight without defeat.
Four clean sheets in five matches helped Rosler's side maintain their play-off push, and Curbishley said: "After narrowly missing out on promotion last season, Uwe Rosler's men are clearly mounting another challenge this campaign. It was an impressive month for Brentford - going unbeaten with some notable results."
Tranmere Rovers striker Ryan Lowe has picked up the player gong for League 1 after bagging five goals, including a hat-trick at Coventry City in an emphatic 5-1 win for Rovers.
He ended the month by scoring a brace in a 2-1 win over Colchester United.
Rovers manager Ronnie Moore said: "Ryan has had a fantastic month and scored some great goals so he deserves this award.
"He didn't have a lot of service early in the season but we're getting the ball in the box more for him now and he is showing what a good striker he is."
In Sky Bet League 2, Southend United's Phil Brown takes the managerial plaudits after leading them through the entire month unbeaten, winning four of their five league matches as well as progressing in the FA Cup.
Goodman said: "Phil is using his considerable experience to lead a Southend promotion push out of Sky Bet League 2.
"Moving from eighth to third in November is a great start. But Phil will be keen to keep the momentum going long into the new year."
Dagenham & Redbridge striker Zavon Hines picks up the player accolade after scoring three times during the month, including the opener in the 2-0 win over Burton Albion.
Dagenham boss Wayne Burnett said: "I'm absolutely delighted for Zavon, he's come here and he really has set the place alight at times.
"The thing that has impressed me most is his incredible work rate, he's got a really hunger and desire."