The Foxes had looked certainties for the drop at the end of the 2014-15 campaign but seven wins in their final nine games saw them pull clear of danger under Ranieri's predecessor Nigel Pearson.
The Italian took charge last summer and guided Leicester to the Premier League title last season, and Ranieri says Leicester must remember how they avoided relegation two years ago to pull away from trouble in the weeks ahead.
The defending champions have been in fine form in Europe and have qualified for the Champions League knockout stages with a game to spare but domestically they have struggled for form.
Leicester are 14th in the standings after Saturday's draw with Middlesbrough, two points clear of the bottom three.
"They must play with the pressure, they must remember how it was two seasons ago. They must play with the same character," he told reporters.
"We must live in two ways. One in the Champions League and one in the Premier League. In the Champions League we are so happy but in the Premier League we aren't happy. Then it's important to be focused on the Premier League.
"The players are human. They are not machines. They remember last season, everyone playing well and everything they tried to do was good. This year no, we have to reconnect their brains."