With Brezovan behind Tomasz Kuszczak and Casper Ankergren in the pecking order at the Amex Stadium, various clubs were interested in securing his services on loan.
However, when Ankergren was injured in training, Brezovan was called up for the trip to Yorkshire and then took his place in the starting line-up after former Manchester United shot-stopper Kuszczak sustained a problem in the warm up.
Poyet said: "I am not going to say the teams but there were three or four interested in Peter.
"But, with that scary situation where you cannot recall him and we have got only two goalkeepers, we were not willing to let him go. Now it's simple, he is going nowhere!"