Moyes' men have been off the pace in the Premier League, going down 3-1 at Chelsea on Sunday to leave the defending champions seventh, while United were also knocked out of the FA Cup at the first hurdle by Swansea City in a poor start to 2014.
The UEFA Champions League and League Cup are Moyes' only realistic hopes of further silverware this term and his charges will need to come from behind to progress in the latter, having been beaten 2-1 by Sunderland in the first leg at the Stadium of Light.
A Ryan Giggs own goal and Fabio Borini's penalty handed Gus Poyet's men the upper hand a fortnight ago and Moyes will be desperate to add the League Cup to the United trophy cabinet - the Scot has already won the Community Shield - and lift some of the gloom around Old Trafford.
United have lost four of their last seven home games in all competitions and will likely need to be on top form for the visit of Poyet's men, who have lost just one of their last 10 outings.
Despite Sunday's setback at Stamford Bridge, Phil Jones remains confident United can salvage something from the club's season - starting on Wednesday against Sunderland.
"I don't think we're a long way away from the teams at the top (of the Premier League)," Jones told the club's official website.
"Now we have to bounce back and we have an important game on Wednesday night.
"We're not a million miles away, I'm telling you, but we need to stick together if we're going to turn it around."
One of the main threats to United's progression is likely to be former Manchester City winger Adam Johnson, who has five goals from his last four games.
After scoring a hat-trick against Fulham a week ago, Johnson was Sunderland's hero on Saturday as he netted the equaliser against Southampton in a 2-2 comeback to earn a point and make it four games unbeaten.
Excluding an unlikely West Ham comeback, progression for either side would set up a final against Manchester City at Wembley, with Sunderland eyeing their first League Cup success and United their fifth.
Despite never having won the competition, Sunderland have reached the semi-finals on three occasions, making the final once back in 1985.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.