The Chiefs, who finished last year with the worst record in the league, have changed coaching staff and brought in the former San Francisco 49ers quarterback during the off-season.
The 28-year-old told reporters: "I think that's the case for every NFL team, and if it's not the case, it's a problem. We're trying to win right now. I think that's the great thing about the NFL.
"You're out there and there are very few perennials. It's a battle every single year. You can go first to worst, worst to first.
"There is so much parity across the league. That's the mindset here, that's for sure. If it's not win now, then that's a problem."
Smith spent eight seasons with the 49ers before being traded to the Chiefs earlier this year.