The deadly duo continued their stunning start to the new Ligue 1 season in a 3-0 win over Bastia on Wednesday night.
Falcao struck late in either half and Riviere was also on target as the unbeaten principality club made it five wins from seven at the start of the new campaign to return to the top of the table, two points clear of champions Paris St Germain.
Falcao and Riviere are Monaco's only goalscorers in the league this season, with the lethal pair combining for 13 goals so far.
Clearly the club might find themselves in trouble if either or both men are hit by injury or suspension, but for now Ranieri is just happy that the good results are continuing to come.
"Maybe we are dependent on Falcao and Riviere, but I am satisfied if they score," the Italian said.
"I am delighted with the performance. The fans of both teams saw a good match.
The two teams had lots of chances and the two goalkeepers made good saves. For 20 minutes it was difficult but slowly we started to find our feet."
Riviere opened the scoring six minutes before the break with a tidy finish on the run to register his sixth of the campaign.
"Riviere scored and he is a different player these days," said Ranieri. "Last year he wasn't good, this year he is. When you have good players, all systems are good."
Monaco doubled their lead on 41 minutes as Joao Moutinho lofted a pass into the area and Falcao ran through to drill home a first-time effort, and the Colombia striker took his season tally to seven in the final minute when he fired in after Yannick Carasco had seen his initial effort blocked.
"It was very important to get the three points and our start to the season has been very good," Ranieri added.
"Results breed confidence, but this is not a message to the other teams. It is too early in the season for that."