Adam Rooney's double and Grant Munro's header were more than enough to see Inverness into the third round of the competition at the expense of their opponents from the Scottish Second Division.
The victory for Caley Thistle made it successive wins following their defeat to Celtic on the opening day of the Clydesdale Bank Premier League season and for manager Butcher it was another good display from his side.
"I'm pleased we got through," he said. "We didn't really get anywhere near the form we showed on Sunday, but credit to Peterhead because they passed the ball well and they frustrated us. "We got the goals at the right times, although it was perhaps slightly disappointing that we couldn't have scored a few more given we created a number of chances."