The Official Charts Company reports that 'Run to You' ended up charting at number 45 for the week, in a list dominated by sales of Gary Barlow's Diamond Jubilee single 'Sing'.
The song, performed by Mitchell upon winning the show on June 2, was placed at number 27 on Wednesday (June 6) but fell drastically in the latter part of the week.
The single's poor performance has been partly attributed to the fact that the track is only available to buy on digital download and has not officially been released as a 'Winner's Single'.
Nevertheless, the failure to chart is in marked contrast to the enduring popularity of singles from TV reality rival The X Factor, and declining ratings for The Voice UK have already led to speculation that there will be a mass shake-up for the second series.
BBC One controller Danny Cohen has admitted that the show has had 'teething problems' but insisted the show is still "fresh" and "exciting".
Photo gallery - The Voice UK final in pictures:
Copyright: BBC/Wall to Wall/Guy Levy
Watch Leanne Mitchell perform 'Run to You' on the Voice UK live final below: