This was a battle of the B teams at White Hart Lane, with a combined total of 20 changes were made by Pochettino and counterpart Stuart Pearce.
Spurs came into the match on the back of a four-game winless streak - which looked set to be extended when Jorge Grant capped his full debut with a second-half goal.
However, Mason's wonderful long-range effort soon brought Pochettino's men level, before a poacher's goal from Roberto Soldado and Harry Kane's stoppage-time attempt eventually saw Spurs run out 3-1 victors.
"We need to be calm after a disaster," Pochettino said, when asked about his emotions having fallen behind.
"No, no, we always believed that we can come back into the game, always believed that it was possible to recover the result.
"Now I am happy, happy for the players because it was a great effort
Never in doubt.
"Going 1-0 down was difficult, but we got a great reaction, an important reaction for our supporters, who encouraged us and backed us.
"It was great after the result
We won and I am happy for the players."
The win sets up a fourth-round home tie with Brighton and means they approach Saturday's north London derby against Arsenal with a much-needed morale boost.
The tie appeared to swing in Spurs' favour after the introduction of Kane and Mason in the minutes following Forest's goal.
Eyebrows were raised at the latter's introduction, yet the 23-year-old marked his fifth appearance for Spurs with a wonderful goal to leave Pochettino confident he has a big future at White Hart Lane.
"Ryan in the beginning of the pre-season was good," he said.
"The last season was difficult for him because he had some injuries, but he is a great talent from the academy
We need to be careful with him.
"He played on Monday for the Under-21s at Sunderland and today he had the possibility to be in the squad.
"He showed his talent and I am happy for him because he deserved this performance and this goal today."
The 3-1 scoreline was harsh on Forest, for whom the defeat was their first in all competitions this season.
Stuart Pearce believes Spurs will be "very relieved" to have progressed to the fourth round and told his players they should leave north London with their head held high.
"I think tactically we got it pretty much right," the Forest boss said
"I think the players - and when I say the players, the whole squad of players - attempt to please you in everything that we impart on them.
"There was a lot of young players on the pitch for us tonight and I thought they did outstandingly well, as well as the senior ones that hadn't played a lot of football.
"We put a team out that we felt was going to win the game and I think Tottenham will be more than pleased that they managed to get through in this competition and not get beaten at home again
They had a big scare.
"From my point of view, I am very proud of them
I am very disappointed we lost the game against a very good side that cost multi millions to assemble.
"A few of our players have given our players a big lift
The fans echoed that tonight, the Forest fans, that made an atmosphere in this game."
Source : PA
Source: PA