United's season slumped to a new low 12 days ago when they lost 2-0 to unfancied Greek side Olympiacos in the Champions League.
David Moyes' men put on a much more impressive display at the Hawthorns on Saturday though, running out comfortable 3-0 winners thanks to goals from Phil Jones, Wayne Rooney and Danny Welbeck.
United looked relatively solid in defence while up the other end of the field, the front four of Juan Mata, Adnan Januzaj, Rooney and Robin van Persie were a constant threat against the free-falling Baggies.
"It was an important day for us, we had to bounce back," the Manchester United midfielder said.
"It feels like such a long time since the last game (against Olympiacos) before the international matches, so we had to perform and really show that we are a good team.
"It's a tough place to come, so to win like we have is a big positive," concluded Carrick.
"We looked dangerous going forward and we defended well. All in all, we couldn't have asked for much more from our performance."
With Tottenham losing to Chelsea and Everton missing from league action this weekend, United's push for a top-four finish now looks in a far more healthy state.
Moyes' men are sixth in the table, nine points off fourth position.
Carrick was happy that United had managed to come away with a convincing result as well as a good performance.
"It's been frustrating this season because, at times, performance-wise we have controlled matches and haven't come away with the results we wanted. You strive for the performances and want the results to follow, and here it did," he said
"We looked really dangerous going forward, we had really good penetration through the pitch and caused them problems all afternoon. We looked exciting going forward."
While Moyes and his players headed back up the M6 with a smile on their faces, Pepe Mel was left to face more questions about his future at West Brom.
Mel was appointed on an 18-month contract in January, but he is yet to win a game in seven attempts and speculation continues that the former Real Betis manager is under threat.
Mel said he did not know whether he would be in charge for Albion's next game against Swansea on Saturday.
The Spaniard has overseen three draws and four defeats during his two-month spell in charge and his team never looked like stopping United.
Albion's defending was poor for all three United goals and goalkeeper Ben Foster was annoyed with the way the Baggies allowed United to take the lead just before the break when Jones peeled off his marker Liam Ridgewell to head home.
"We came in at half-time 1-0 down again," Foster told West Brom's website.
"We need to stop doing that. We can't always come in 1-0 down and then try to grind something out, nick a goal and get something out of the game.
"It's something we need to look at. We have a week's training ahead of us now and we will look at it before the Swansea game."