Coetzer's side bowled England out for 365 after posting their highest one-day international score of 371-5 as Calum MacLeod batted 140 not out from 94 balls to conclude the win for the Scots.
The result is Scotland's first win over their southern neighbours in the previous five ODI fixtures between the two countries, and Coetzer was very happy with his team on the day.
"It is a hugely special day for us," Coetzer told reporters.
"Creating history is what our coach (Grant Bradburn) framed these games against England and Pakistan as and that's what we've done. I am extremely proud of [our comeback] but it is a trait that we are starting to get very, very good at. With the ball in our hand, we have been exceptional over the last couple of years and for this to be our first game of the year it has been an outstanding performance.
"In the first powerplay, wherever we moved a fielder Bairstow hit the ball somewhere else. He struck the ball cleanly right from the start of his innings. I was just hoping he would mis-hit one. Thankfully that happened!"
Scotland will face Pakistan next in two T20s on Tuesday and Wednesday.