Ms Sturgeon told Sky News, Mr Miliband needed to be more than just a pale imitation of David Cameron.
She said: "I get a strong sense that people really want change. So there is an opportunity at this election to deliver change.
"Ed Miliband knows as well as me that if there is an anti-Tory majority, the only way David Cameron gets back into Downing Street is if Ed Miliband is prepared to stand back and let him back in.
"If he does that, then Labour voters in Scotland will never forgive him and I suspect Labour voters across the UK would never forgive him."
In an opposition leaders' TV debate on Thursday, Ms Sturgeon repeatedly called on Mr Miliband to work with her party to "lock" the Tories out power.
But the Labour leader argued they had "profound differences" and said he could not be in coalition with a party leader who wanted to break up the Union.
Ms Sturgeon on Friday told Sky News: "We are not talking about a coalition. Let's think about 8 May.
"If Ed Miliband and the SNP between us have more MPs than David Cameron has, is Ed Miliband really saying he will stand back and not work with the SNP, he's just going to watch David Cameron go back into Downing Street?
"If that is his position, let him come out and say that."
Her comments came as Mr Cameron warned a deal between Labour and the SNP would mean more borrowing and taxes.
In a Twitter post, Mr Cameron said: "Ed Miliband won't rule out a vote-by-vote deal with the SNP so he can be PM. It would mean more borrowing and more taxes and you would pay."
Pressed over the SNP leader's offer, Mr Miliband said: "My message to Nicola Sturgeon is 'thanks, but no thanks'."
He added: "It's not going to happen. I will never compromise our national security, I will never compromise our commitment to fiscal responsibility, I will never compromise on the nature of our United Kingdom."
Mr Miliband had used the opposition leaders debate to challenge Mr Cameron, who did not take part, to a "one-on-one" showdown.
But Mr Cameron dismissed the call, pointing to the 146 weekly exchanges they have had at Prime Minister's questions.
A poll by Survation/ Daily Mirror indicated Mr Miliband won the debate with 35%, while Ms Sturgeon came a close second on 31% with UKIP's Nigel Farage on 27%.
All those taking part in the debate rounded on Mr Cameron for not taking part.
But the PM said he was "not invited" and also repeated his warning that Labour backed by the SNP "would break up Britain and bankrupt Britain".
He added: "I think you saw on your television screens last night just a hint of the chaos you would get from that sort of coalition."
Mr Farage has also told Sky News he had "no regrets" over his remarks during the debate in which he claimed the audience were biased, resulting in him being jeered.
He argued the studio audience were "way out of line" with public opinion.
Meanwhile, back on the campaign trail, Mr Miliband has promised to end the "scandal" of long-term internships, and Mr Cameron warned of the threat to the Conservative "jobs miracle" if Labour gets back into office.
Lib Dem leader Nick Clegg travelled to Gordon, Scotland, where ex-SNP leader Alex Salmond is vying to wrestle the seat from his party.
Mr Clegg has appealed to Labour and Tory supporters to vote tactically to prevent Mr Salmond "dancing off to strut his stuff on the Westminster stage".