The Colombian striker's time at Manchester United has so far been undermined by injury issues since his loan move from Monaco.
But making his first start since October 5 on Saturday, Falcao netted for the second time in a United shirt to earn a 1-1 Premier League draw at Villa Park.
And Carrick believes his impressive header could prove to be the catalyst for a rich vein of form.
"He's scored so many goals over the years and you always feel that when he gets that chance he will score,” Carrick told MUTV. "He's scored a terrific header again and I'm pleased for him.
"After being out for a bit that's him back and hopefully he can go on a bit of a streak for us and we, as a team, can return to winning ways and get on a roll again.
"Things are going okay, although we hoped for more [at Villa], but we didn’t lose and hopefully we can carry that on over Christmas and be stronger for it when we come out on the other side in January."
Louis van Gaal's side face Newcastle United at Old Trafford on Boxing Day and travel to Tottenham two days later.
