Two goals from Jamie Vardy gave the league leaders a 2-0 win away to Sunderland which put them 10 points clear of second-placed Tottenham, having played one game more.
Vardy and Danny Drinkwater claimed after the match that the victory felt like a crucial one, with Leicester now three wins away from the most unlikely of title triumphs.
Ranieri was moved to tears as he applauded the travelling fans at full-time but warned that they cannot now allow their focus to slip.
"We knew it would be tough, it is normal because Sunderland are fighting to be safe, but I am very happy for the three points," he told BBC Sport.
"Our performance was very solid, of course they had the chance to draw but we had three or four chances to finish it early.
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"The fans must continue to dream but we must continue to be concentrated and focused. Now we have two tough matches at home, the Champions League is on the table and we have to keep it. We achieve nothing yet.
"We have to stay calm, be focused, strong, solid and keep going. You make this job for the emotion you feel inside but it is difficult for me to tell what kind of emotion. Today we made some mistakes, we still have to look at what is not right."
Vardy ended a run of six league games without a goal to move onto 21 for the campaign, and Ranieri admits he was relieved to see his leading scorer rediscover his clinical touch.
"It is important for Jamie Vardy to score because he made some good assists in the last game but he is our goalscorer and he needed to score again and I am very happy with him," he added.