Charity Children 1st has called for Hearts player Craig Thomson to be sacked after he was put on the sex offenders register.
The 20-year-old has been convicted for indecent behaviour towards two girls aged 12 and 14 on the internet.
The club said they were keeping the player as there were mitigating circumstances which provided assurance his conduct would not be repeated.
Children 1st insisted Hearts need to look again at the issue.
The charity's policy manager Kate Higgins told BBC Radio 5 live: "We believe that Hearts football club needs to look again at this situation, not taking action to protect children from the risk of sexual harm is unacceptable.
"Allowing convicted sex offenders to continue working where they will have direct and indirect contact with children is wrong."
Thomson was placed on the sex offenders register earlier this month after pleading guilty to two charges of indecent behaviour.
He was also fined £4,000 for his lewd, libidinous and indecent behaviour towards two girls, aged 12 and 14, over the internet.
Hearts said it would go through the "necessary internal procedures relating to the case".
On Friday the Scottish Premier League club said Thomson's "grave error of judgement" was due to "naivety and possible wrong outside influence".
The full-back resumed training at the club with immediate effect.
He issued an apology via the club website, saying that he is "fully aware that I have let everyone down".
Hearts posted two statements on the matter on their website. The first read: "The club views this matter very seriously and does not condone the behaviour of the player. Appropriate action to prevent any further development of unlawful activities has been taken.
"In reaching this decision, the club accepted that there are sufficient mitigating circumstances that provide significant assurance that the player's conduct, no matter how distasteful, was the result of a grave error of judgement due to naivety and possible wrong outside influence rather than anything more sinister and it will not be repeated."
Then, early on Friday evening, the club issued another statement which refers to "outside influences on players and the club".