The Red Devils moved three points clear of rivals Manchester City on Monday evening after defeating Fulham 1-0 at Old Trafford.
City faltered in the race for the championship over the weekend having to settle for a point against Stoke City, after Yaya Toure cancelled out Peter Crouch's superb opener.
Both sides have just the title to play for this season after crashing out of both domestic and European cup competitions.
And the former Fulham man is determined to win some silverware this season after helping United become champions in his first season with the club.
Furthermore, Smalling highlighted the importance of coming out on top over City, saying: "We're both Manchester clubs. That's bragging rights for a whole year. We can't let that happen!
"They are not used to playing for just one trophy at United. The Champions League is gone. We are all disappointed about that.
"But we have to make sure we get that Premier League trophy in the bag. It was great to win it last year, in my first season with the club.
"It would be even better to win two in a row, especially when you see people like Ryan Giggs and Paul Scholes have won it 10 or 15 times. It's not that they brag about it or anything, but it makes you think. We have to make sure we are on our toes all the time."
Smalling has found first-team opportunities in his favoured centre-back position limited this campaign due to the fine form of team-mate Jonny Evans.
The England man has been utilised at right-back by manager Sir Alex Ferguson and he admits he is not afraid of competition for starting places.
"That just drives you on. The competition makes you raise your game. Jonny's come in and done really well. But I knew he was here when I came," he added.
"You have to deliver each week. Long-term I see myself as a centre-back, that is where I hope I will play, but I'll play wherever the manager asks me too.
"We had injury worries at the start of the season. But I'd only ever played centre-back when I joined, and I'm pretty sure that's where they see my future."
