The prime minister did not deny making the comments, in October last year, as he argued against a second lockdown.
But he told Prime Minister's Questions the government was making "incredibly tough balancing decisions" at the time.
Nothing he could say or do would make up for the "loss and suffering" people had endured, Mr Johnson added.
The prime minister said the "median age" for those dying was "above life expectancy", in a What'sApp message leaked to the BBC by Mr Cummings, the PM's former adviser, adding: "So get Covid and Live longer".
Labour leader Sir Keir Starmer said: "Will the prime minister now apologise for using those words?"
Mr Johnson, who is self-isolating at his Chequers country retreat, replied: "Nothing I can say from this virtual despatch box or nothing I can do, can make up for the loss and suffering people have endured in this pandemic."
He highlighted the public inquiry into the pandemic, promised for next spring, and said ministers had been faced with "incredibly tough balancing decisions", weighing the "catastrophe of the disease against the suffering that is caused by lockdowns".
Sir Keir replied: "I think we need to check that the line at Chequers is working because the prime minister's answers have no resemblance to the questions I am actually asking him."
The SNP's leader at Westminster, Ian Blackford, also called for an apology, adding: "How can anyone have put faith and trust in a prime minister who actually typed the words 'Get Covid and live longer'?"
And he repeated his call for an immediate public inquiry into the government's handling of the pandemic.
'Summer of chaos'
Mr Johnson said it was "right" that the inquiry should start in the spring when the country would be in a "much better position", adding: "That doesn't mean that we aren't continuing to learn lessons all the time".
At the final PMQs before Parliament goes into recess, Sir Keir warned of a "summer of chaos" amid confusion over government policy on exemptions for people pinged by the NHS app and Covid passports for nightclubs.
"When it comes to creating confusion, the prime minister is a super-spreader," said the Labour leader.
"Why is it OK to go to a nightclub for the next six weeks without proof of a vaccine or test, and then from September it will only be OK to get into a nightclub if you've got a vaccine ID card?"
Sir Keir said Mr Johnson's new three-word slogan should be "get a grip", amid reports it will be "keep life moving".
Mr Johnson accused the Labour leader of trying to "score cheap political points".
"Everybody can see we have to wait until the end of September, by which time it is only fair to the younger generation, when they will all have got the two jabs, before we consider something like asking people to be doubled jabbed before they can go into a nightclub.
"That's blindingly obvious to everyone, it's common sense."
Mr Johnson said it would also "encourage" younger people to get jabs.
Shortly after Prime Minister's Questions, Labour announced that Sir Keir would be self-isolating for a fourth time.
"One of Keir's children tested positive for Covid this lunchtime. In line with the rules, Keir and his family will now be self-isolating," said a Labour spokesperson. "Keir was already doing daily tests and tested negative this morning. He will continue to take daily tests."