It was a match which began with Darren Fletcher at right-back in the absence of Nemanja Vidic, Rio Ferdinand, Jonny Evans and John O'Shea and following the early exit of Brown and Neville - with a groin problem - United were left fielding an unfamiliar back-four.
Ryan Giggs was forced into playing at left-back, while Patrice Evra was pushed into the middle of defence to partner Carrick.
"Evra must be the smallest centre-half in the world, but he's a good reader of the game. He's quick and determined," Ferguson added.
UNITED'S INJURY WOES
Gary Neville (groin)
Nemanja Vidic (flu)
Rio Ferdinand (calf)
Jonny Evans (calf)
John O'Shea (thigh)
Rafael da Silva (injury)
Fabio da Silva (groin)
Edwin van der Sar (knee)
Wes Brown (limped off)
Owen Hargreaves (knees)
The Scottish boss will be delighted to pick up three points to close the gap on league leaders Chelsea - especially after the Blues defeat at Manchester City - but the lack of defensive options could hamper his team's prospects in the near future with Edwin van der Sar also on the sidelines.
United need a point against Wolfsburg to top Champions League Group B and help avoid a clash with a bigger side in the next round.
On choosing his defence against the German opposition, Ferguson added: "Probably Nemanja Vidic will be back from flu and I'll probably play Carrick alongside him.
"Carrick's got the composure and the pace and it was a good performance in the second half. We used our experience."
West Ham boss Gianfranco Zola was left frustrated after more than matching the Premier League champions until Scholes's crucial strike.
Carrick happy to help out defence
"The first goal scored changed the story of the game," the Italian boss said after seeing his side concede their 10th goal in three league games.
"We were defending well and they didn't create much. We have no complaints - our players gave everything. When you play the champions it's always difficult and if you give them something they will exploit it. The second goal killed us."
As well as dealing with their leading striker Carlton Cole missing for several weeks, Zola had to endure an early substitution for goalkeeper Robert Green (feeling sick) and Zavon Hines (knee problem).
"I might have to put my boots on again," he added. "Right now we are short. We didn't pose enough threat to them. But remember they are the champions and we had young players in our team."
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