The Gers were 1-0 up at the break thanks to a first-half goal from Lewis MacKinnon but despite dominating possession, they were unable to add to that until strikes from Alex Lowry and Cole McKinnon in the second-half.
Speaking to RangersTV after the match, King said: "I thought we started the game in the first-half a bit slack and unlike us but I think that was down to Edinburgh being well-organised and well-drilled and it was hard to break them down.
"Once the game started to get on we found a lot more gaps are we able to play our game. The pitch suited us and the way we wanted to play but with them sitting in a low block it made it difficult for us.
"It was just a matter of being patient and working passes and trying to play round them but we got there in the end."
King was pleased to also keep a clean sheet, as he captained the Gers this afternoon.
He added: "It was just a matter of being patient we know the chances are going to come and if the chances do fall to anyone in the team in the right place I trust them to put it away.
"It is good to get another clean sheet. Winning games and scoring goals is good but keeping a clean sheet week in week out is also key for our team."