Scotland dream of end to 18-year wait
Having let slip a 21-5 lead to trail Ireland 21-22 midway through the second half, two penalties in the last eight minutes by captain Greig Laidlaw secured Scotland's first victory in an opening Six Nations fixture since they beat France at Murrayfield in 2006 – potentially putting them in contention for their first Championship title in 18 years.
"It certainly changes the dynamic," said Cotter, who is aiming to finish his three-year tenure on a high before making way for Glasgow coach Gregor Townsend in June.
"You can feel it. You start the Six Nations with a win and everybody speaks about it.
"But it's only one game. I know the feet will be on the ground very quickly come Monday morning, just to make sure we back this up with another good performance."
Next up for Cotter's side are France away next Sunday and Scotland have not won in Paris since 1999, when Townsend inspired them to their last Championship success, in the final year of the Five Nations.
They will certainly travel with renewed confidence, having rocked Ireland, who beat the All Blacks in November, with a dynamic first half performance that yielded two tries for the brilliant fullback Stuart Hogg and a cunning score directly from a line-out by centre Alex Dunbar.
"The last time we were in Paris we were close to winning," said Laidlaw, referring to a 16-19 loss in a World Cup warm-up in September 2015.
"We can take heart out of that and I think we've moved forward even since then.
"We'll enjoy this tonight [Saturday] and we'll get our feet back on the ground tomorrow morning [Sunday]. We'll not get ahead of ourselves."
Asked if Scotland's target for the championship had been changed by the victory, Laidlaw (who returned a perfect place-kicking record, with three conversions and two penalties) replied: "We want to win the next game. If we win the next game, we'll be in a good position."
Laidlaw will head to the Stade de France with added personal incentive – he moves from Gloucester to Clermont at the end of the season.
Cotter will also join a French Top 14 side – Montpellier – but for the time being the New Zealander is savouring his first win over Ireland coach Joe Schmidt, his former assistant at Bay of Plenty and Clermont.
Asked whether the victory was the best of his international stint with Scotland, Cotter said: "It has to be."
In contrast, Schmidt was lamenting a false start that might cost his team dearly in the Championship race.
"We arrived 15 minutes late and we were late for all things in that first half," said Schmidt. "We were sluggish. The key thing is we've got to start better in Rome next week.
"Defeat is tough to take but it was always potentially a reality coming here. The Championship looks tough to win but we're not out of it.
We backed up with a bonus point and we've got to go to Italy and make it six points and make sure we’ve got some momentum in this Championship."
Although a try and conversion by stand-in flyhalf Paddy Jackson put Ireland ahead – following tries by wing Keith Earls and lock Iain Henderson – Schmidt's side sorely missed the orchestrating of the injured Jonathan Sexton.
"Jonny could come into it for next week but the more time Paddy gets in the Six Nations the better he'll be," said Schmidt.