Just over a fortnight ago, Scotland kicked off their autumn Test series with a 31-14 defeat by Eddie Jones' side at Murrayfield before they lost again at the weekend in Glasgow, although the margin of defeat was slightly narrower at 31-17.
But the 24-year-old refused to concede that the Scots will simply never be good enough to challenge the top-class nations ahead of their clash with South Africa on Saturday.
He said: "We do believe we will beat them one day, absolutely.
"When we were preparing for the Test games everyone in the squad thought we could win and so we're disappointed that we never won either of the two games.
"In the game at Hampden we played more good rugby in that than in most of the other meetings. We started reasonably and then let it slip away.
Scotland coach Williams has made two changes to his team for Saturday's Test.
Chris Paterson wins his 50th cap, while captain Gordon Bulloch equals Kenny Logan's record as second most-capped Scotland international on 70 appearances.
Jason White returns while Allister Hogg moves to number eight.
South Africa coach Jake White believes Scotland's recent spirited performances against Australia prove they are a force to be reckoned with.
He said: "I have watched videos from their Six Nations campaign, the summer tour Down Under and the two games against Australia recently.
"We must be underdogs, we lost last time we were here, we are playing away from home and they did really well in the two Tests against Australia.
"They have always been one of the best rucking teams in the world, the way they recycle the ball and the way they keep it going."
White has made seven changes to his starting XV for the game.
Gurthro Steenkamp and Solly Tyibilika will make their Test debuts while Bryan Habana will start his first Test match.
Jaque Fourie, Wayne Julies, Danie Rossouw, CJ van der Linde all come into the side while Schalk Burger and AJ Venter, Eddie Andrews, Breyton Paulse and De Wet Barry are all out.
Scotland team: H Southwell; C Paterson, B Hinshelwood, A Henderson, S Lamont; D Parks, C Cusiter; A Jacobsen, G Bulloch, G Kerr, S Grimes, N Hines, J White, A Hogg, D Macfadyen.
Subs: R Russell, B Douglas, S MacLeod, J Petrie, M Blair, G Ross, G Morrison/ South
South Africa team: P Montgomery, J Fourie, M Joubert, W Julies, B Habana, J van der Westhuyzen; F du Preez; G Steenkamp, J Smit (capt), CJ can der Linde, B Botha, V Matfield, S Tyibilika, D Rossouw, J van Niekerk.
Subs: D Coetzee, O du Randt, G Britz, J Cronje, M Claassens, G Bobo, G du Toit.