The Frenchman, 26, beat his Italian rival in straight sets but was not pleased with his performance.
"It was not a really good level from me," he told reporters afterwards. "I didn't play, you know, really well. But today I did the most important [thing], which was to win."
Tsonga said "an ear problem" caused by exposure to air conditioning meant that he struggled to move around on the court.
"It was difficult to have a good balance," he explained. "I caught a cold a few days ago because of air conditioning and my ear gets plugged sometimes. In that case I can't hear from one side and I have the impression I'm losing my balance on the court, so it bothered me a little bit."
Tsonga now goes on to face Bernard Tomic in the second round.