Flares were set off by some Wakefield fans after Paul McShane scored a try in the game, which Trinity won 24-22 after a dramatic comeback.
The club statement reads:
“Wakefield Trinity Wildcats would like to express extreme disappointment at the actions of the supporters who tarnished the image of the club on Sunday.
“The 1500 or more travelling supporters behaved impeccably throughout the game but were let down by the actions of a small number of individuals who, if identified, will be banned from the club, ground and with the will of other parties, the sport of rugby league, throughout the world.
“If you have any information on the individuals involved then please contact the club via email@example.com or via phone on 01924 211 611. Confidentiality will be maintained at all times.
“The sport of rugby league and the Wakefield Trinity Wildcats RL club are appalled by their actions and both are committed to a sport characterised by on pitch rivalry and off pitch respect.
“The club will work alongside Castleford Tigers and the RFL to conduct a full investigation into the incident.”