While Rush admitted that his side were deservedly beaten, he accused Alibert of ruining the game.
"Taking nothing away from Wakefield, they're in great form and deserved the win, but I'm sick of being involved in games like that when he's refereeing," said Rush.
"He kills us. Every time we've had Thierry Alibert in a game this year we've ended up in situations like that.
"I appreciate I'm going to get in trouble for it, but every single time we have this guy, he hammers the game."
St Helens are currently third in the Super League table - above Leeds Rhinos and Catalans Dragons on points difference - with two matches remaining.