The U's reached the fifth round last season but any repeat of those heroics were dashed by ten-man United.
George Maris was shown a second yellow card for the hosts after 40 minutes but just before half-time Jabo Ibehre put Cambridge ahead.
The National League side battled valiantly in front of over 500 travelling fans and Kieron Cadogan hit the woodwork in the second half in search of an equaliser.
Sutton boss Paul Doswell told the club's website: "I thought the performance was outstanding, we tried everything we could with the substitutions and went very brave in the last half an hour to get something out of the game.
"That's us and Lincoln gone from last year, that's football. You have the big hitters, who get to the quarter final and fifth round respectively, and then today we couldn't have done anymore.
"We put that many crosses into the box, you're just hoping something's going to fall. You have to give Cambridge United a lot of credit, they defended for their lives like lions in the box. We never really got that unbelievable opportunity where your head is in your hands.
He added: "It didn't help us them going down to ten because they sat even deeper. It could have gone either way, that game. It was a good FA Cup game. I thought both teams gave it their best.
"The one benefit of not being in the FA Cup is that you can concentrate very much on the league and also have a good go at the Trophy."
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