Goals from Mbuemo (38') and Bruno Fernandes (81') sealed the result against a ten-man Spurs, who had Cristian Romero sent off after 29 minutes.
There has been a massive improvement in the team's form following Carrick's appointment and he will be gunning for a fifth straight win when they face West Ham away on Tuesday.
Reflecting on the game, the Cameroon striker explained that his side have been building their current form all season but concedes the mentality is a lot stronger than under former head coach Rubin Amorim.
He said in the Manchester Evening News: "I just feel we built on what we were doing from the start because I don't think it was that bad as a lot of people felt.
"We just worked together, make the effort together, with a big mentality, and we're never beaten. Even if someone gets past, we come back to support and just try to give it all.
"We just want to take it game by game, train as hard as possible and yeah, we just want to keep working as a team."
Mbuemo now has nine goals and one assist in 20 Premier League games.
When asked to explain his goal celebration, the player added: “I need to think of a new one now! My one has been seen many times now, so I'm going to find a new one.”