Saracens, warming up for a crunch Pool 3 Heineken Cup clash with four-time champions Toulouse in France in the new year, were 49-10 winners, scoring six tries. It was a crushing setback for the visitors, who had won their previous six matches.
The 28-year-old Flood missed the trip to Allianz Park, but his next start will be his 100th of his career with Tigers.
"Toby rang me and said he has decided to go and do other things. I suspect probably in France," explained Cockerill. "He is our club captain, and he will be our captain until the end of the season. There is a long way to go and a lot of things to do.
"We have had lots of situations where guys move on and the good ones, and Floody is certainly one of the good ones, make their decision and concentrate on playing and we will try to win the Aviva Premiership and do what we can in the Heineken Cup.
"Floody has been great for us and he will continue to be great for us for the rest of the season. We put our best offer forward but I don't think it's a monetary thing, he wants to do something different and sees his chances with England being limited.
"We've lost some very big names from this club in the last 20 years but have been OK. Toby will go but we'll cope with it. Nobody is bigger than the club.
"You'd like to think Leicester is an attractive place to come to. We are looking at several options and I'm sure we'll find someone to do the job for us."