"I'll focus on my match, I'm playing tomorrow", Sharapova said; "But nothing is a disappointment after being away from the game for 15 months".
Lucic-Baroni edged Czech Lucie Safarova, 7-5, 4-6, 6-3.
The Russian's 6-4 6-2 triumph over Christina McHale in Rome sees her move into the world's top 200 and secure a qualifying berth at the All England Club - but should she reach the semis in Italy this week, Sharapova would be set for a place in the main draw at Wimbledon.
Sharapova showed some signs of a slow start as she failed to find her first serves, allowing McHale to exploit those vulnerable second serves of her, breaking serve to 30 in the opening game and taking the early lead.
Even that could be avoided if she reaches the semi-finals in Rome, which would take her to a ranking of around 100 and get her directly into the main event.
Several other players have criticised the decision by tournament organisers to welcome Sharapova back so readily.
Should the 30-year-old three-time Rome champion, ranked 211 in the world, reach the semi-finals, she would nearly certainly earn an automatic Wimbledon main draw slot ahead of the May 22 rankings cut-off date.
The qualifying tournament is held the week before, in the quaint surroundings of Roehampton, in south-west London - potentially creating a security headache if Sharapova plays.
In the men's draw, ninth seed David Goffin of Belgium came from behind to beat Brazil's Thomaz Bellucci, 6-7, 6-3, 6-4.
McHale, ranked 58th, faded badly in the second set as Sharapova hit her stride, producing glimpses of the talent that took her to world number one.
The German two-time Grand Slam champion was forced to quit while trailing Canadian Eugenie Bouchard but arrived in Rome on Sunday ready to play in the last big claycourt event before Roland Garros begins on May 28.
It is still unknown if the five-time Grand Slam victor will be handed a wildcard into either qualifying or the main draw at the upcoming French Open, and the two-time Roland Garros champion will discover her fate on Tuesday.
"I've had a lot of treatments". Incredibly, Sharapova is already one of the favourites to win the French Open.