"We were average and that wasn't enough to trouble Lille," Ligue1.com quotes Antonetti as saying.
"We were good defensively, but were unable to put them in danger when we attacked. We weren't good enough and not determined enough. We were well organised but timid."
Midfield playmaker Alessandrini was stretchered off in the 35th minute with a suspected cruciate injury, and the 51-year-old coach admitted that it would be a bitter blow if the worst were confirmed.
"The worst news was Alessandrini's injury," he added.
"We can make up for losing a match. But if he's snapped his cruciate then that's really bad news for him and for us, that's for sure."
Rennes will try to bounce back from defeat against Sochaux next Saturday.