Centre Tuilagi and lock Deacon departed during the closing stages of a game Leicester won 32-13 that extended their unbeaten Premiership run to five matches.
"They have both got hamstring strains of various degrees," Cockerill said.
"We are not sure to what extent at this stage. During the course of the 24 to 48 hours, we will know."
Deacon, Leicester captain in the absence of a rested Geordan Murphy, scored one of his team's four tries as Tigers climbed to fifth place, level on points with their next opponents Sale Sharks.
England fly-half Toby Flood ran the show by contributing 17 points, including a try, while wings Matt Smith and Horacio Agulla also touched down against a Worcester side twice reduced to 14 men after number eight Chris Jones and then substitute prop Oliver Tomaszczyk were sin-binned.
Cockerill added: "It is not an easy place to come and play and get a result, so to win and get a bonus point is fantastic for us. I am delighted.
"We made a massive start (Leicester led 17-0 after 22 minutes), which was something we had talked about all week. A big start was important, and we got that.
"We've got Sale, who are another difficult side, on Sunday, then Wasps at home. We've got to keep trying to collect the points."
Leicester are now lurking just outside the title play-off zone, climbing further away from the Premiership's lower reaches that they occupied during much of September and October when they had a dozen players on World Cup duty in New Zealand.
They lost five out of six league games during that World Cup period, but since it ended, Tigers' Premiership record shows four wins, one draw and no defeats.
"The World Cup period was very hard for us," Cockerill said.
"We had a lot of guys missing, and we got caught out. We had to bite our lip and take some medicine. That happens sometimes.
"But we have kept the faith in how we want to play and we've kept our bottle, and we have started to turn it around.
"With 12 Test players missing during the World Cup, plus eight or nine injuries, you are going to have problems, and we got beaten. People have to judge us when we have a full complement of players."
Worcester briefly threatened a revival when wing Marcel Garvey scored early in the second half. Fly-half Joe Carlisle's touchline conversion, added to a couple of earlier penalties, saw Warriors just 20-13 adrift.
But ultimately, they were made to pay for a dreadful start when Flood twice cut them open defensively, creating Leicester's opening try for Smith and then scoring himself.
"We showed a lack of urgency at the start," Worcester head Richard Hill said. "We were slow to react and we lacked a period of continuity.
"We had identified that Leicester don't play with too much width, so we knew we had to mark Flood and the areas around him, but what did we do? We let him right through the middle.
"He had to be bottled up, but we didn't do that. We did not stick to our defensive strategy during the first 20 minutes, and those first 20 minutes killed us.
"Of all the games this season, that was one of our most disappointing. I am not happy with it. We under-performed, it is not good enough and we need a reaction."
Worcester now head to Wycombe for an appointment with Wasps next Sunday, still just six points and one place above bottom club Newcastle.
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