In strikingly outspoken comments, the Prime Minister said he was not prepared to overrule the House of Lords Appointments Commission (Holac) or make promises to key allies of Mr Johnson about becoming peers.
"And if people don't like that then tough," Mr Sunak said at a fintech event in London.
But the PM was himself being urged to show how the Conservatives could win the next election with their "best player off the pitch", after Mr Johnson's resignation as an MP on Friday.
The Tories trail Labour by a double-digit gap, according to polls, far more than when Mr Johnson was in No 10.
MPs on the Commons Privileges Committee were today meeting to decide when to publish the findings of their inquiry into whether Mr Johnson misled Parliament over partygate.
Former culture secretary Nadine Dorries, ex-minister Nigel Adams and Cop26 president Sir Alok Sharma were reportedly put forward by Mr Johnson for peerages. Ms Dorries and Mr Adams have resigned as MPs since being omitted from the peerages list, leaving Mr Sunak facing three by-elections.
One of Mr Johnson's allies accused the PM of a "deceitful slight of hand", claiming No10 had interfered in the nominations list.
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