The SFA say Danny Wilson would have served the suspension sparked by his League Cup final red card during a Premier League game in England.
Inverness last night sought further explanation over why the on-loan Liverpool defender was allowed to play against them on Saturday despite leaving Scotland with an outstanding League Cup ban.
The 21-year-old set up Michael Ngoo's goal in the 1-1 draw at Easter Road on Saturday before Hearts won on penalties to secure a final place.
Wilson played in the 2010 final for Rangers and was sent off for denying a goalscoring opportunity in a 1-0 victory over St Mirren, sparking a one-match ban in the competition, but signed for Liverpool before Rangers began the defence of their trophy.
Wilson made his Liverpool debut in the Anfield team's opening League Cup game of the 2010-11 season, a penalty shoot-out defeat in September against a Northampton team featuring Inverness striker Billy McKay.
But the SFA say there was no outstanding suspension when he returned to Scotland earlier this month.
A spokesman said: "The player did have an outstanding one-match League Cup suspension when he left Rangers FC to go to Liverpool FC in 2010.
"When the International Transfer Certificate was issued to the FA, this suspension was notified to them, as per FIFA regulations.
"It was then for the FA to apply the suspension in accordance with their own rules.
"The FA does not operate competition specific disciplinary procedures so the suspension would have been served in Liverpool FC's opening league match of season 2010-11 against Arsenal FC (the player did not play in this match).
"There was no outstanding suspension notified to the Scottish FA when the ITC was issued for the player coming back to Scotland.
"Therefore the player was eligible to play in last Saturday's League Cup semi-final."
Inverness made enquiries over Wilson's eligibility yesterday but were not entirely satisfied with the outcome.
In a statement last night, the club said: "As a result of discussions that have taken place throughout the afternoon, the club will be seeking further details and an explanation on events surrounding this matter."
But Hearts manager John McGlynn today admitted he was surprised the issue would not go away.
McGlynn added: "All I can say is that we are aware of that and we asked for clarification from the SFA and they told us that Danny didn't have any suspension and was eligible to play and that's what happened, and that is how we see it after checking again and again and again.
"Hearts have done nothing wrong at all."
