The Scottish Conservative leader, who saw his party match its best ever result at a Scottish Parliament election maintaining the 31-seat total it won in 2016, said both Scottish and UK government needed to work together to make devolution work.
He also claimed that he had campaigned to block a second referendum only because the SNP had put the holding of a new vote at the centre of its campaign.
Speaking on BBC Radio Scotland he said: “The Scottish people voted in an election for the parliament to use the powers it has and another referendum is clearly outwith the remit of the Scottish Parliament. The people I spoke to were voting on recovery, protecting jobs, improving educational standards, supporting the economy and getting us through this health crisis.”
He added: “I had to put an independence referendum at forefront of our campaign as the SNP put it at the forefront of theirs, and while Nicola Sturgeon also said a vote for the SNP was not a vote for another referendum before the votes were counted and seats declared the SNP were out talking about another referendum. Where has the comment been from Nicola Sturgeon about protecting people’s jobs, improving the economy? Not a single word since she has been elected again.”
Asked about comments by re-elected Galloway and Dumfries East Tory MSP Finlay Carson that his party had to accept the SNP’s success and his belief that parts of the devolution system were broken, Mr Ross disagreed.
“I agree the SNP is the government here in Scotland, though they failed to get an outright majority and I think people expect all politicians from all parties to now focus on recovery. She [Nicola Sturgeon] may be saying now is not the time, but she’s used every opportunity on the airwaves to only speak about another independence referendum.
“I don’t believe devolution is broken, it works when our two parliaments work together. Scotland has representation both at Holyrood and Westminster and it would work better if the two governments worked together.”
The Scottish Conservatives lost two constituencies on Thursday, with Ruth Davidson’s seat of Edinburgh Central going to the SNP’s Angus Robertson and John Scott losing his Ayr seat after 20 years to the SNP's Siobhian Brown.
However the party’s campaign focused heavily on list votes, and the two losses were offset by two gains on regional lists, including in Highlands and Islands where Mr Ross was one of four Tory MSPs elected.
Tactical voting is also believed to have helped contribute to an increase in the Tory's share of the vote in the election.
Mr Ross’s comments on Nicola Sturgeon's position were echoed by Scottish Liberal Democrat leader Willie Rennie who said: “Before polling day Nicola Sturgeon promised the recovery would come first but all she has talked about since is independence.
“People who voted for the SNP but are opposed to a referendum will be concerned about how the First Minister is using their support. She must keep her word and put recovery first.”