The Premier League champions went four top-flight games without victory over the end of November and beginning of December, including back-to-back 1-0 defeats at Old Trafford to Everton and Newcastle United.
United have improved in their last two fixtures, however, beating Shakhtar Donetsk 1-0 in their final UEFA Champions League group stage fixture before comfortably seeing off Aston Villa 3-0 in the league on Sunday.
And manager Moyes has now targeted continued improvement, with United looking to make the League Cup semi-finals for the first time since winning the competition in 2010 in their visit to the Britannia Stadium on Wednesday.
"It (our play) continually has to improve and it will improve," he told Sky Sports in the aftermath of the Villa victory. "I'll make sure it gets better in the coming month."
United have seen off challenges from Liverpool and Norwich City to make it this far, and will be confident of claiming the scalp of Mark Hughes' side, with Stoke having never beaten Manchester United in the Premier League.
Indeed, Stoke's last victory over United in any competition came in a 2-1 League Cup triumph in September 1993 thanks to a double from Mark Stein.
However, at that time, ties in the competition were staged over two legs and United progressed courtesy of a 2-0 success at Old Trafford.
Former United striker Hughes is looking to orchestrate Stoke's best performance in the competition since their 2-1 triumph over Chelsea in the 1972 final.
Stoke have twice reached the quarter-final stage since then, most recently in the 2008-09 season when they lost 1-0 to Derby County.
The Britannia Stadium outfit head into the fixture on the back of two draws and a win in the top flight, with 0-0 stalemates against Cardiff City and Hull City sandwiching a superb 3-2 success over Chelsea.
Centre-back Robert Huth (knee) is ruled out for Stoke, while United will definitely be without Robin van Persie (thigh) and Michael Carrick (Achilles).
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