Mazzarri, suspended in January, was sent off for pushing rival forward Nilmar during the Group A match against Villarreal on December 7, which his side won 2-0 to progress to the last 16 at the expense of Manchester City.
The score was goalless at the time and Mazzarri later said that his gesture calculated to try and shake up his own team.
UEFA said that its appeals tribunal partially admitted a cross-appeal from UEFA's disciplinary inspector, who had asked for a stiffer sentence.
Mazzarri's ban was lengthened to three matches although the enforcement of the final game was suspended for a probationary period of two years.
The 50-year-old coach will be barred from the touchline and his team's dressing room for the matches against Chelsea on February 21 at home and March 14 away.
He is also prohibited from talking to his players and technical staff before and during the match, even by phone.
Earlier this season, Arsenal coach Arsene Wenger was banned for two European games for breaching the terms of a previous ban by talking to his staff by mobile phone.
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.