"I don't think I played as well as I could have, so I'm not satisfied at all," said the 22-year-old American.
"I had opportunities to close the match out earlier and I think the scoreline could have been a little different."
Mauresmo, a three-time beaten finalist here, produced a scintillating display to defeat 1994 Wimbledon champion Conchita Martinez in straight sets.
Mauresmo's victory over the 32-year-old four-time Rome champion set up a meeting against 10th seed Silvia Farina Elia, who beat Russian 17-year-old Maria Sharapova in her second match of the day to ensure there would be two Italians in the quarterfinals.
Farina Elia, who defeated American Meghann Shaughnessy in her rain-delayed second-round match in the day's early action, joined compatriot Francesco Schiavone in the last eight.
American fifth seed Jennifer Capriati, winner of three Grand Slam titles, lost just four games in her straight sets demolition of Argentine Paola Suarez in her third-round match.
A trouble-free 6-2, 6-2 victory set up a quarterfinal clash against Israeli 16th seed Anna Smashnova-Pistolesi, who defeated Italian wildcard Flavia Pennetta.
Mauresmo, 24, said she had to be aggressive to prevent Martinez taking control of the match.
"I tried to use a little power because if you give her time and let her dictate the game she can punish you," Mauresmo said.
Mauresmo, who has always reached at least the quarterfinals here since her first appearance in 1999, said her good record in Rome was down to her preparation.
"The good thing about coming here is that I've usually played a couple of tournaments beforehand and sometimes even more," she said.
"I always come here with a lot of matches behind me. It helps my confidence and my rhythm on clay."
Attack also proved to be the best form of defense for Capriati.
"I felt like I was playing really well, hitting my shots, serving well and even coming to the net a few times," said the 28-year-old American, who reached the semifinals here two years ago.
"My mentality was to go out there and go forward. When I am moving well I can get to the ball that little bit quicker. And at the net you need that little bit extra to make the difference."
Kuznetsova, a quarterfinalist at Wimbledon last year, booked her place in the next round by edging Japanese seventh seed Ai Sugiyama in a tense three-set battle.
Kuznetsova threw away a 5-0 lead in the decider to allow Sugiyama to draw level, but the 18-year-old Russian held her nerve in the tiebreak.
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