The Foxes pulled off a great escape last season, winning seven of their final nine games to stay up under Nigel Pearson.
They became just the third team in Premier League history to survive after being bottom at Christmas.
And ahead of the season opener at home to Sunderland, the Italian said his side must be prepared for another scrap.
“The Premier League is very hard, we are a little team but we want to be bigger,” the 63-year-old said.
“In my career I’ve seen it is more difficult in the Premier League in the second year than the first year. I want us to play at the same level we played in the last eight or nine matches because they were fantastic.
“One draw, a loss against Chelsea, and all wins.
“I think they were the best team in the league for the last eight matches.
“Why? Because they have a big heart on the pitch. I saw one man, together.”
The former Chelsea boss said he will assess the fitness of new signings N’Golo Kante and Yohan Benalouane before the weekend.
Ranieri was appointed after Pearson was sacked in June after falling out with the board.