They have a chance to redress the balance at Murrayfield on Saturday when they take on the Barbarians in a non-cap international and second-row Murray said after Monday's squad announcement: "We just want to play well against the Barbarians and hopefully a win will come from that.
"All the guys are massively proud to play for Scotland and they are keen that the fans keep believing in them.
"It's going to be a long road but we are definitely going to get there, knowing what young lads are coming through.
"They are stronger, fitter and faster than I was when I was a young fella so we just urge them to keep supporting us because we will get there," he added.
"I am massively excited about the tour and playing the Barbarians, especially with all these young guys around me. It's a massive challenge for us on Saturday, there are a lot of new guys and we are treating it like a Test match."
Murray, 28, said that there were positives to take from their 37-16 defeat against Ireland in their final Six Nations match of the season as Scotland went in search of a first win against the Barbarians, rugby union's most prestigious invitational side. "The way we started to perform at the end of the Six Nations was pretty good and we played pretty well in patches against Ireland," Murray said.
"Hopefully we will get a bit of confidence and move onto bigger and better things. If we can get our line-outs and our scrums working it's definitely possible that we could win but we just want to go out there and play well."
Scotland squad. Backs: Graeme Beveridge (Glasgow), Stephen Cranston (Borders), Chris Cusiter (Borders), Simon Danielli (Bath/ENG), Andrew Henderson (Glasgow), Gareth Morton (Borders), Dan Parks (Glasgow), Chris Paterson (Edinburgh), Tom Philip (Edinburgh), Simon Webster (Edinburgh) Forwards: Gordon Bulloch (Glasgow), Bruce Douglas (Borders), Iain Fullarton (Sale/ENG), Scott Gray (Bath/ENG), Andrew Hall (Glasgow), Allister Hogg (Edinburgh), Alastair Kellock (Edinburgh), Cameron Mather (Glasgow), Euan Murray (Glasgow), Scott Murray (Edinburgh, capt), Steve Scott (Borders), Tom Smith (Northampton/ENG).
AFP - 2004.
