Ms Sturgeon, who was mentioned several times in the debate despite not taking part in it, said she did not believe either man was fit to be PM "on the strength of these performances".
Scotland's relationship with the rest of the UK featured heavily in the television showdown - with Mr Johnson accusing his Labour rival of having already done a deal with Ms Sturgeon to win the keys to Number 10.
While Mr Corbyn said there would be "no support for a Scottish referendum" on independence in the early years of a Labour government, the Prime Minister accused him of plotting a "chaotic coalition" with Ms Sturgeon, the SNP leader and Scottish First Minister.
Mr Corbyn branded that "nonsense", saying: "There will never be a coalition between Labour and anybody else. There are no deals that have been done, and there will be no deals that are done."
He added: "I have said there would be no deal with the SNP, there would no support for a Scottish referendum in the early years of the next Labour government because I want to invest in
Scotland and give Scotland the £70 billion it needs in capital investment."
Ms Sturgeon was not involved in the debate, organised by broadcasters ITV, after a legal challenge on Monday failed to win the party a place in the head-to-head contest
She said afterwards: "The clear takeaway for Scotland from this debate is that neither of these men should be able to determine Scotland's future.
"Jeremy Corbyn can't decide if he is leave or remain and Boris Johnson is determined to take Scotland out of the EU against our will."
The First Minister insisted: "Only a vote for the SNP in this election can help Scotland escape from Brexit - and secure our right to choose a better future as an independent country."
And she said she "wasn't impressed with either of the leaders", adding: "I don't think either of them are fit to be prime minister, certainly not on the strength of those performances tonight."
Scottish Labour leader Richard Leonard said: "This debate could not have made clearer the choice facing Scotland in this election.
"We can face another five years of cuts, chaos and deception with Boris Johnson - or we can vote for hope, investment and a fair society with Labour and Jeremy Corbyn.
"Over the coming weeks we will be taking our positive message to every workplace and every community."
The Scottish Conservatives, meanwhile, questioned Mr Corbyn's commitment to the Union between Scotland and the rest of the UK.
While Mr Johnson had described the Union as being "the most important thing", Scottish Tory leader Jackson Carlaw said it was "incredibly revealing" that the Labour leader had failed to do make the same commitment.
Mr Carlaw warned: "Quite simply, if Mr Corbyn becomes Prime Minister, the Union is in immediate danger."
Speaking about the Labour leader, he said: "He didn't campaign in Scotland during the independence referendum and he has shown again tonight that he thinks Scotland is expendable."
Liberal Democrat Chirstine Jardine said Mr Corbyn had "refused to rule out Indyref2" and had also "refused to commit his party to campaign for remain" if there was a second Brexit referendum.
"Only the Liberal Democrats can be trusted to both campaign to stop Brexit and oppose IndyRef2," she stated.