Thackray re-signed for Hull from Leeds on 27 March
Hull have been fined £100,000, £40,000 of which is suspended for 12 months, for fielding an ineligible player in the Challenge Cup.
They were punished for playing Jamie Thackery in two games before he was placed on the club's cup roster.
Thackery was re-signed from Leeds after the initial 3 March deadline and played in the wins over Rochdale and Widnes.
Hull have seven days to appeal after being found guilty of a breach of the Rugby Football League's rules.
The prop forward played in Hull's 42-5 fourth-round win at Rochdale on 20 April, but the blunder only came to light after he also appeared in Hull's 32-18 fifth-round win over Widnes.
Hull escaped expulsion from this year's competition, but when the incident first came to light the RFL said the breach was a "very serious matter" and suggested that the competition's rules would be tightened up to prevent a reoccurrence.
The east Yorkshire club are due to play Wakefield in the Challenge Cup semi-final at Doncaster's Keepmoat Stadium on 27 July for a place in the final against either Leeds or St Helens at Wembley.