The president has also said his compatriots failed in their responsibility to protect Cecil.
Cecil the lion was killed last month by American dentist Walter Palmer.
Robert Mugabe said Zimbabweans should protect their natural resources from what he called foreign “vandals”.
In a speech for National Heroes Day he said: “Even Cecil the lion – he is yours. He’s dead!”
Cecil – a favorite at Hwange National Park – died after he was shot by Walter Palmer using a bow and arrow.
The dentist from Minnesota has said he believed the hunt was legal.
It is thought Walter Palmer paid about $50,000 to hunt 13-year-old Cecil, who wore a GPS collar and was being studied by Oxford University for conservation purposes.
Robert Mugabe used a speech in Harare to make his first public comments about the lion, whose death sparked international condemnation.
The president said: “He was yours to protect and you failed to protect him.
“There are vandals who come from all over of course… some may be just ordinary visitors, but [there are] others who want to vandalize, to irregularly and illegally acquire part of our resources.”
Prosecutors have said the lion was shot with an arrow after being lured out of its protected zone, and died from a bullet wound inflicted 40 hours later after it had suffered major blood loss.
Zimbabwe is battling to curb illegal hunting and poaching which threatens to make some of its wildlife extinct.
The country is seeking Walter Palmer’s extradition.
Some commentators have criticized the attention that the death of an animal has received when the nation has endemic poverty and unemployment, and political strife and repression are commonplace.
Much of Robert Mugabe’s speech was spent remembering those killed in the struggle for independence.
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