"Of course we'll listen and reflect, it's too premature to say what we'll do next around that".
She added: "Folk might remember I fought a leadership election on the other side of that particular argument".
Scottish Conservative leader Ruth Davidson is believed to have personally helped persuade the Prime Minister that she could cause real damage to Miss Sturgeon's campaign by creating a "referendum on another referendum".
The party also lost two of their biggest names in Westminster - Depute Leader of the party Angus Robertson and former First Minister Alex Salmond.More news: South Africa : West coast storm kills 8, causes chaos
She went on to criticise Theresa May, who called a snap election in a bid to boost her party's slender majority at Westminster - a gamble which spectacularly backfired on the Conservative leader.
"Clearly in the last few days of this campaign we saw a surge towards Jeremy Corbyn, which we saw in parts of Scotland, as well as across the rest of the United Kingdom", she said.
The Labour party, which used to dominate Scottish politics, was reduced to just one Scottish lawmaker in 2015.
But given the scale of the SNP's recent triumphs, Thursday's vote was a sizable setback for a party unused to such hindrances.
The reports were seen as a sign that the party's Scottish leader was seeking to assert the influence of her MPs.
The SNP suffered losses in what were, until very recently, heartlands, particularly in rural Scotland.More news: Third London Bridge attacker named
Professor Iain Begg, of the London School of Economics, said it had been a "disastrous" election for the SNP. Ironically for a party that opposed the creation of a Scottish Parliament in the 1997 referendum, a little devolution has now gone a long way for the Conservatives.
The SNP still took 35 of Scotland's 59 seats in Britain's 650-seat national parliament, while the Conservatives won 13 Scottish seats, achieving the second largest share of the vote.
With the Tories having lost their majority, she said the SNP would "work with others, if it is at all possible, to keep the Tories out of government". We'll make sure Scotland's voice is heard in the Brexit negotiations, and we will continue to stand up for Scotland's industries, including fisheries and agriculture.
"The SNP tsunami of 2015, in which the party took 56 of Scotland's 59 constituencies, was followed yesterday by an quake in which the SNP lost more than a third of their MPs", says Alex Massie in The Times.
Scotland's Finance and Constitution Secretary Derek Mackay, who directed the SNP's election campaign, told the same programme: "The First Minister has said that she'll reflect on the result but the fact that another Tory government that Scotland has not elected will rule over us with policies that Scotland just doesn't support I think has been another lesson on why Scotland should have a choice".
Ms Davidson said the UK Government must "seek to deliver an open Brexit, not a closed one, which puts our country's economic growth first".More news: Millwall fan who tackled London terrorists a 'hero' - Carl Frampton