The former Blues midfielder guided the club to Champions League qualification in his first season in charge, but more is expected this time out after a spending spree in the transfer market.
Lampard admits that he came to the club "to win" and feels the arrivals of the likes of Timo Werner and Ben Chilwell "changes the landscape".
He said: "I didn't come into the job to fight for fourth place or bring academy players in; I came here to win.
"Last year we couldn't recruit and this year the club have made the decision to bring in players. It changes the landscape and we're ready to work."
The 42-year-old coach added: "The pressure on me to do better should be standard. I don't want to talk about statements.
"Last year, we were very happy for Champions League places. We were very joined up in the business we wanted to do.
"I am surprised if you didn't think I wasn't under pressure last season. I thrive off the pressures. It's what I love doing."
Lampard revealed that he will be without three of his new recruits - Hakim Ziyech, Chilwell and Thiago Silva - for Chelsea's season opener against Brighton.
He said: ''[Hakim] Ziyech took an injury to his knee in the friendly against Brighton, he won't be fit. We're working with him and hoping it's a matter of weeks. We'll have to see on that one.
"Ben Chilwell is working towards fitness but won't be fit either, but he's improved which is good news for us. Thiago Silva is in London but not training with us until the weekend. I doubt very much he'll be in contention."