The Tangerines host St Mirren in the last 16 at Tannadice with the aim of getting back to winning ways having not won in their last seven league outings.
United were in top gear until St Mirren inflicted a 4-1 defeat on them on Boxing Day and they have not won since.
But McNamara believes they are still in decent fettle going into their televised match with the Buddies.
McNamara said: "Our results might not have been great recently but we're not playing all that badly.
"We believe that one win could change everything and we just need to keep on doing the things we're good at.
"We were getting a lot of good publicity before this run but there's no lack of confidence.
"We've got faith in the players and we know what they're capable of on their day.
"Hopefully they can come good on Sunday as it's a match that means a lot to the club."
United got to the semi-final of the competition last year before losing to eventual winners Celtic at Hampden.
McNamara hopes they use that experience to their advantage when Danny Lennon's side come to Tannadice as they attempt to repeat their 2010 cup-winning efforts.
He said: "We got a taste of it last year.
"Everyone wants to win trophies and we're no different.
"The lads here are hungry and we can hopefully benefit from what happened last season.
"There's always a big carrot there for any team wanting to get far in the cup.
"We know the winners will go into the quarter-finals. We don't need any more motivation than that so come Sunday we will be raring to go."
McNamara is calling for the home fans to act as their extra man and help drive them on a cup run.
He said: "The fans have been great this season. We want to give them success as they deserve it.
"They can play their part as well by getting behind the lads as they always do."
St Mirren manager Lennon is excited about the impact of new signing Eric Djemba-Djemba.
The former Manchester United midfielder could make his debut against United if he proves his fitness ahead of the clash.
Lennon has brought the 32-year-old in to strengthen the central midfield and allow flair players such as Paul McGowan and Kenny McLean to go forward with confidence.
And he feels the Cameroon international can also boost his side's passing game.
Lennon, who signed Djemba-Djemba on Wednesday after the former Aston Villa, Odense and Hapoel Tel Aviv player was released by Partizan Belgrade, said: "His name came up and he excited me.
"We did our due diligence and we liked where he has been for the last three to five years.
"He has played a lot of football within that.
"He has still got ambition as a 32-year-old. He wants to get himself out there and give himself every opportunity to go to the World Cup and we can give him a platform to build on that.
"He has vast experience. He has played in World Cup finals, he has played Champions League, he has played Confederations Cup, he has won the African Nations Cup, and he is ambitious enough that he wants to go to another World Cup.
"He will give us that balance of defending when we are attacking, and - along with Jim Goodwin in there - I am delighted to have that experience.
"He is a lovely passer of the football as well. And that sits well with our philosophy."
- Sports & Recreation
- St Mirren
- Danny Lennon