James Rodriguez, Emmanuel Riviere and Lucas Ocampos were on the scoresheet as Monaco strengthened their grip of third spot, closing to within two points of leaders Paris Saint-Germain.
Ranieri, whose big-spending side are in the top flight after being promoted last season, said challenging PSG was too big of an ask.
"I think it is very difficult to put any pressure on PSG at the top. They are a team which is capable of winning the Champions League," he said.
"For Monaco it is our first year back in Ligue 1 and it is important to continue at this level.
"We are only looking at ourselves and our results, not looking at the other teams."
Ranieri reserved special praise for Rodriguez, who appears to be settling in after a difficult start to his time in France.
The Italian said Colombia international Rodriguez was improving in the attacking midfield role he wants him to play.
"James Rodriguez is someone who can play either on the left or the right wing," Ranieri said.
"However, for me I believe his best position is to play behind the strikers. He is starting to fit into the team now in that position so I will leave him there.
"For me a number 10 has to be able to see the whole game, he has to be able to score goals and also make the final pass.
"At the start of this season, James Rodriguez didn't understand what I wanted him to do, or maybe didn't understand the French league at first.
"However, he is a smart player and now he has started to play very well for us. He works very hard for the team not only when we have the ball but also when we lose it to win it back.
"The whole team have been working hard to recover the ball."
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