David Goodwillie's hat-trick helped the Taysiders beat Partick Thistle 4-1 in their third-round clash at Tannadice on Wednesday night to join Hearts, Aberdeen, Motherwell, Hibernian, St Johnstone, Morton and Inverness in the hat at for Thursday draw at Hampden.
McNamara acknowledged his former side's shock home loss to Championship side Morton on Tuesday night has left the trophy up for grabs.
He said: "The tournament has opened up and I'm looking forward to the draw.
"I'm delighted to be in it as this was a tough tie against Thistle.
"Everyone left in it will say they're capable of winning it.
"There's a real good opportunity (for clubs), ourselves included."
Goodwillie, the on-loan striker from Blackburn, had only scored once since returning to United from the Lancashire club in the summer.
But he was the difference between the two sides, opening the scoring in the 33rd minute with a drive before heading in just before the break.
By the time he knocked in his third in injury time, United substitute Ryan Dow, on for Brian Graham, had scored a third for the home side before Christie Elliott scored a consolation for the visitors.
McNamara said: "I never doubted he was capable of that. I'm delighted for him.
"I hope scoring three goals can be a turning point for him.
"The fourth goal, especially, was a great finish after a great bit of play from Ryan Gauld and a ball across at pace from Stuart Armstrong.
"There's been a lot of pressure on him to come up here and perform.
"Hopefully the other boys - like Nadir (Cifti), Armstrong and Gauld - chipping in with goals has taken a bit of weight off his shoulder and the goals will come. I hope there's more to come."
Jags boss Alan Archibald bemoaned a couple of first-half slips which handed United the advantage.
He said: "If your strikers aren't scoring you have to keep clean sheets and we made a couple of errors.
"Conrad (Balatoni) slipped for the first goal which was disappointing because he had a good performance and we lost a goal from a set-piece.
"But apart from that we were the better team."