The Swansea City defender, 28, arrived in Glasgow with a Capital One League Cup winners' medal following a 5-0 victory over Bradford City at Wembley last month.
Williams was also still basking in the glory of Wales' record 30-3 rugby union win over England at the Millennium Stadium at the weekend which clinched the RBS Six Nations title.
With a nod to Cardiff's lofty position at the top of the npower Championship, Williams looked forward to riding the crest of the sporting wave into the Group A game against the Scots.
"I was thinking about that the other night when I was watching a replay of the rugby game," he said.
"Everyone is still buzzing, rugby is a massive sport in Wales and it was a great day for everyone concerned.
"I thought it would be nice if we could get a win as well and keep the momentum going in Wales and give the public something to cheer about again.
"Swansea have had a good season, Cardiff are top of the league so it would be nice if we could carry that on and that is what we will be looking to do tomorrow [Friday] night.
"Playing against Scotland gives it a little extra as well being a home nations game and both countries will be desperate to win."