The Ligue 1 newcomers made it four wins from five Ligue 1 matches thanks to Radamel Falcao's sixth-minute penalty at the Stade Louis II.
However, Ranieri lamented the number of mistakes his side made during the clash and believes Lorient could have snatched a draw.
"I am a little bit angry as we made too many mistakes, we did not pay enough attention on our passing and didn't raise our game," the Italian said.
"It was important to have the possession of the ball. We won 1-0 against Lorient but they did create many chances, it was a tight game."
Ranieri believes his side made life difficult for themselves during the clash, citing a Falcao chance that was not taken in the second half as a missed opportunity.
"We were in control for most of the game and in the end it was more complicated," Ranieri said.
"I am satisfied with the way we played except for some bits during the first half. I think that Falcao had the opportunity to score the second goal. Lorient also had one or two opportunities to score thanks to (Yann) Jouffre."
Ranieri's side face champions Paris Saint-Germain at the Parc des Princes in their next Ligue 1 fixture on Sunday.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.