The world number three took the first set 6-4 but lost the next two sets against the 16th seed on tiebreaks (7-2) (7-4) in a superb match of clean-hitting strokes.
"I should never have lost this match," the 16-times Grand Slam champion told reporters. "He knows how close he came to losing. I had multiple chances but I couldn't make the difference.
"I thought I was playing well but he served better towards the end and hung in there. I didn't feel I could break and it's no fun to play like that," said the Swiss, who was knocked out by Ernests Gulbis in the second round in Rome last year.
"I'm looking forward to a few days to stay mentally and physically fresh and practice very hard. The same thing happened last year,"
World number one Rafa Nadal returned to form with a 6-4, 6-2 win over compatriot Feliciano Lopez despite almost withdrawing with a fever while fourth seed Andy Murray also progressed beating Potito Starace of Italy 6-2, 6-3.
World number one Caroline Wozniacki targeted Grand Slam success after overpowering qualifier Anastasia Rodionova of Australia 6-2, 6-0 in the Italian Open second round on Wednesday.
The Dane will next face Belgian Yanina Wickmayer, who came back from a set down to defeat 13th seed Ana Ivanovic 2-6, 7-6, 6-3.
In other matches, third-seed Victoria Azarenka of Belarus crushed local Sara Errani 6-1, 6-2 to set up a clash with Russian Anastasia Pavlyuchenkova. Fourth seed Li Na skipped past Spaniard Lourdes Dominguez Lino 6-4, 6-2.
Fifth seed Jelena Jankovic was sprightly enough in dispatching Czech Lucie Safarova 6-0, 6-3.
Lee-Hesh exit
Third seeds Leander Paes and Mahesh Bhupathi crashed out after being outplayed in the super tie-breaker by American pair of Sam Querrey and John Isner.
The Indians lost 3-6, 6-3, 5-10 to their unseeded rivals in the second round in one hour and 12 minutes to make an early exit.
