Smith, signed from Oldham in the summer, has scored five goals in 15 appearances this season but started on the bench in the weekend win at Charlton when Blackstock, on loan from Nottingham Forest, made his first Leeds start.
"There's seven strikers at the club," said Smith. "So there's a lot of pressure when you go out on the pitch to impress and prove.
"Dexter's come from a big club like Forest, so he's going to be here to play. It's up to me to keep him out of the side and keep me in it.
"I'm here for the same reasons. It's all healthy at the end of the day."
Smith, one of the tallest players in the Sky Bet Championship, has made an impressive step-up from League One after bursting on to the scene for Oldham last season with goals in the FA Cup against Liverpool and Everton.
"There aren't too many 6ft 6in strikers in professional football at the moment," he added. "You could probably count them on two hands.
"It's a bit of a dying breed so when you do get thrust into the first-team environment, you are going to get stereotyped and people accuse you of being a bit one-dimensional.
"But it's none of my concern. My concern is to improve. I know within myself what I need to work on and hopefully Leeds can bring the best out of me.
"A lot of people are quick to judge weaknesses but it's sometimes a case of playing to your strengths.
"I definitely know what mine are, but at the same time I want to work on my weaknesses to get them up to speed."