United have changed managers three times since Ferguson brought down the curtain on his trophy-laden 27-year reign at Old Trafford in 2013.
While both David Moyes and Louis van Gaal failed to lead the club to a top-three finish in the league, Carrick thinks things are starting to click into place under Jose Mourinho.
“It was never going to happen overnight, I don't think we were ever going to suddenly move on so quickly,” Carrick, who joined the club in 2006, told reporters.
“Sir Alex had been here so long. It doesn't happen overnight and everyone just forgets about it, but there are certain signs that we are getting there. I can say that.
“I know we are well away in the league, but there are signs that we can feel something is coming. Time will only tell with that, though.”
United have drawn five of their last seven league games and stand sixth in the table, 11 points off the pace.
They beat West Ham United 4-1 on Wednesday to reach the League Cup semi-finals, however, having inflicted a 4-0 defeat upon Feyenoord in the Champions League on Nov. 25.
“There have been occasions in the cups where ... the goals have gone in. It hasn't quite happened in the league... but if we keep playing like that, we will be okay,” the 35-year-old said.
“It is not something where you just flick a switch... you have to build as a team... I think we will be all right.”
United visit Everton in their next league game on Sunday.
Original source: Carrick sees signs United moving on from Ferguson era