World No. 60 Nick Kyrgios, meanwhile, complained that the courts are "too slow."
Mannarino was forced to retire against Roger Federer after slipping in the fourth set and injuring his knee, while Williams appeared to slip and hurt herself during a return in the first set against Aliaksandra Sasnovich.
After receiving medical attention, Williams then buckled at the baseline midway through a point and gingerly walked off the court in tears, later saying she had a right leg injury.
"Brutal for @serenawilliams but centre court is extremely slippy ... Not easy to move out there," tweeted two-time Wimbledon winner Andy Murray, who had played on the tournament's main show court on Monday.
Federer, who reached the second round through Mannarino's retirement, learned of Williams' injury during his press conference.
"It feels a tad more slippery maybe under the roof, I don't know if it's a gut feel," he told reporters.
"You do have to move very, very carefully out there, and if you push too hard in the wrong moments, you do go down ... this is obviously terrible. I don't think it plays very different but again I'm also moving carefully."
Federer, who is bidding to win a ninth title at Wimbledon, will face two-time semifinalist Richard Gasquet in the second round.
Following the two incidents, which happened just an hour apart, the All England Lawn Tennis Club said in a statement to CNN: "The preparation of the grass courts has been to exactly the same meticulous standard as in previous years.
"Each grass court is checked by the Grand Slam Supervisors, Referee's Office and Grounds team ahead of play commencing, and on both days of the Fortnight they have been happy with the conditions and cleared the courts for play.
"The weather conditions on the opening two days have been the wettest we have experienced in almost a decade, which has required the roof to be closed on Centre Court and No.1 Court for long periods.
"This is at a time when the grass plant is at its most lush and green, which does result in additional moisture on what is a natural surface."
Kyrgios, a man never afraid to speak his mind on the tennis court, had a separate complaint about the grass.
During his match against Ugo Humbert, which was suspended with the score poised at 6-4 4-6 3-6 6-1 3-3, Kyrgios said into a courtside camera: "Guys, for you watching at home, it should be fast in here ... They've made it slow. This isn't grass anymore."
Kyrgios' match against Humbert will conclude on court number one on Wednesday.
CNN's David Close contributed to reporting.