"As a life long Stranraer fan, I think everyone can be assured that there was no ulterior motive."
David Longmuir, chief executive of the Scottish Football League said: "The SFL has a duty to the teams involved to correct the error and to protect the integrity of the draw."
When asked why the draw was not redone, Longmuir told BBC Sport: "We looked at all the options.
"But we felt the draw was done in the proper manner and decided to stick with the sequence in which the balls came out."
First Minister Alex Salmond helped make the draw, televised live at lunchtime on BBC Scotland, and he said: "As soon as the mistake was realised Alex Fergusson did the right thing by owning up and moving to correct the genuine error straight away.
"Once football fans are over the shock, I am sure even Hearts fans like myself will have a wry smile and get down to planning for the semi-final."
The Rangers versus Hearts match will be played at Hampden and the other tie could be staged at Tynecastle or Easter Road.
The ties will be played on 29 and 30 January, although it has not yet been confirmed which matches will take place on which night.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.