The singer released a rendition of 'Run To You' following her victory on the singing contest earlier this month (June 2).
However, after little promotion during the show itself and lack of a physical release, the single only managed to reach number 45 on the UK chart.
"It's been a week and it hasn't had a chance to do anything yet," Mitchell told the Daily Star of the position.
The vocalist signed a record deal with Universal Music as part of her prize for winning The Voice UK and is expected to release her debut album later this year.
"I'm hoping we're going to get a good balance between my own songs and cover versions," she explained, when asked about her hopes for the record.
Meanwhile, the BBC declared the first series of The Voice UK a hit after it announced it was its biggest entertainment launch in a decade.
The talent show achieved a consolidated series average of 9.2 million (38.5% share) viewers, meaning it was more successful than the first series of The X Factor, Strictly Come Dancing and I'm A Celebrity.
Watch Leanne Mitchell perform 'Run To You' below: