Thiago Motta struck a 34th-minute winner against Chievo as Inter finally gave their fans something to celebrate having failed to win in their previous four home matches in all competitions.
"It was important to get rid of the 'San Siro taboo', although it seems strange to say it, but we hadn't won here or scored here," Ranieri told Inter's official website.
"The team was solid and determined. They really wanted this victory with all they had.
"We knew it wouldn't be an easy game but it went well, against a team that has a good collective play and runs a lot. I'm satisfied.
"Teams like Chievo make all the big teams suffer a bit, but we locked up the three points at home. Now our thoughts are on Atalanta [away on Wednesday] another difficult team to face."
Inter are currently 16th in Serie A and eight points behind leaders Udinese. Ranieri has not given up on the Scudetto yet this early in the campaign.
"Coaching Inter, of course you have to believe in it [winning the Scudetto]," he said.
"Let's not forget that up to December the team are the world champions [having won the Club World Cup last year], and so of course we must stay up there."
Inter are starting to play into some form again as they followed up Tuesday's 1-0 UEFA Champions League win at Lille with Sunday's win over Chievo.