United swept their Third Division opponents aside with skipper Jon Daly scoring in between a double from Johnny Russell at Tannadice.
"The result gives everyone a lift," McNamara said on Sky Sports 1. "I know we have got potential. The front three were very sharp today.
"We've got some good players here and hopefully we can kick on now. It's the first step today."
The result was never in doubt after Russell's opener just 15 seconds into the tie and United were sharper all over the pitch.
McNamara praised the Glasgow side for a strong performance after the break, until United's superior fitness eventually paid off with Russell's second goal and the dismissals of Rangers duo Kal Naismith and Ian Black in the last 11 minutes.
"Rangers were possibly the better team in the second half but we defended well," McNamara added.
"It was eight games without a clean sheet before today so that was a plus for us."