"I felt we dominated that first half, a lot of that was through how we defended as well as how we attacked - it's a message for our players that we can play at that level and create more opportunities".
Bruised by a chastening defeat at home by England last week, defending Six Nations champions Ireland - the 2018 World Rugby team of the year - needed a reaction at Murrayfield. Scotland also lost three throw-ins.
"We are relying on others, but when it comes to next week [in Italy a week on Sunday] and the final two rounds we don't have to rely on them for how we approach things and how we perform", Schmidt said.
Ireland admitted they were not fully mentally prepared for the physical onslaught against England - but after Saturday's edgy Edinburgh win, captain Best believes they have restored the right mindset.
But after a breathless first half in which the Irish edged 12-10, they scored a third soft try for some breathing room and their defense limited Scotland to just a penalty.
The New Zealand-born fly-half - who moved to Munster a year ago after being an understudy to Sexton at Leinster - made a nervy start with his pass being intercepted leading to Scotland's try at the end of the first-half.
Carbery nearly gave Scotland its only try from an intercept, but he created the only try in the second half and kicked a penalty to deny the Scots even a losing bonus point at home.
"There was definitely a rise in temperature, definitely a rise in energy, from last week", Schmidt said.
The try was a double blow to Scotland. However, replacement Joey Carbery was excellent, not least when lofting a superb long pass to Keith Earls for the try that seemed to kill off Scotland. What changed in the 15 minutes of half time?'
Scottish hooker Stuart McInally was more gracious in defeat praising the Irish for their resolute defence.
"I think that was the first knock and then he got another one after that. He got a stamp on the ankle and it was really when they were going on to treat that that they decided he wasn't 100% and that they needed to do a HIA and he didn't pass". "We'll need to be at our best if we are to win over there".