The Perth side posted a loss of £200,000 this week and chairman Steve Brown has said that player funds would be affected as a result.
However, Wright has said that he was aware of the situation and is happy with the squad that he has assembled.
"[The chairman] was quite open with me when he offered me the job," he told STV.
"He told me what the budget would be and I knew the budget would be cut substantially. But that's the situation that Scottish football is in and I've come into the job with my eyes open.
"With the work that the chairman has done I think we've put a good squad on the pitch for less money this season. The most important thing is the stability of the club and the future of the club."
Wright replaced Steve Lomas as St Johnstone boss during the summer.