The defender is looking forward to coming up against his former club Fulham on 26 January after the Cottagers squeezed past Blackpool on Tuesday.
"Before this game, we knew we'd get a home draw and whoever it was against would be strong opponents," he told MUTV. "I saw some highlights of the Fulham game [at Blackpool] and it will be a nice game come Saturday week. At least we're at home and we fancy ourselves.
"It does mean a lot. I know Ryan Giggs and Paul Scholes [and Darren Fletcher] are the only players who have won it and Rio and others have emphasised how important it is that they want to get on it. We want to help that."
Smalling was outstanding alongside Phil Jones in the 1-0 win with both centre-backs earning praise from Sir Alex Ferguson afterwards.
"All the defenders know each other as we play a lot together in training," he said. "We've not played too much together in matches but we're both centre-halves and both out there to do a job.
"It's the third time we've played them this year and we knew exactly what to expect. You can stop giving away cheap fouls but you know it's coming into the box at one stage and everyone needs to stand up for themselves.
"We're starting to pick up a couple of clean sheets, which is nice. The whole team defended well and, luckily, we kept a clean sheet."
The 22-year-old reserved special praise for his captain on the night, Ryan Giggs, who rolled back the years with another vintage display.