The Blues have signed Raheem Sterling from Manchester City but Tuchel knows that more high-calibre players must arrive with the top-flight looking competitive ahead of the new season.
The coach told Sky Sports News: "The stakes are high and we're competing not only against the best teams who have ever played in the Premier League but also the best coaches.
"If you [then] see the transfer period and quality of coach at Tottenham, if you see the same at Arsenal, at Man Utd, we know what the challenge is. It's the toughest challenge you can [have]."
Tuchel admits that things are even more tricky for Chelsea as they are under new owners - led by US businessman Todd Boehly - and are recovering from the sanctions placed on former Russian owner Roman Abramovich.
He said: "We come from sanctions, we come from losing top-quality players, key players, we are a club in transition, in transition of ownership, we were behind in the transfer race and we were behind in the table. So we have things to improve.
"We love to compete and we love the challenge at the very top. For that we need signings of new quality players or otherwise there's no chance."
Chelsea have been linked with a move for Cristiano Ronaldo but Tuchel says his focus is to refresh Chelsea's backline at the moment.
The German coach said: "I would not rule it out [signing another striker] but right now it is not the priority. The priority right now is defence, it's not a secret. From there we need to see what's possible."