The 31-year-old suffered a blow to his face during Thursday's game and is now certain to miss the Celtic clash on March 29.
"It was fantastic being part of such a great team performance on Thursday night.
"This is the worst possible thing that could happen after breaking back into the team.
"Hopefully I'll get back as quickly as possible so I can help the team to win trophies.
"I know I'm out of the next leg but I know my team mates can finish the job," added Cousin.