But he admits he was surprised by the centre forward’s decision to join big rivals Crystal Palace.
Poyet takes his in-form team to Selhurst Park tomorrow with Murray on a prolific streak.
He has hit 15 goals in 16 outings this season, including two home hat-tricks and seven in his last three appearances at Selhurst.
Murray, 29, quit Albion for Palace for a 75% hike in wages in May 2011 after spearheading the Seagulls’ League One title success with 22 goals.
His controversial departure has baffled some supporters, as Albion continue their long search for a target man but Poyet told The Argus: “It’s simple, at that time we couldn’t pay him within our budget. We were not able to pay that amount of money at that time. “He was our top scorer. You don’t let your top scorer go away for free but we couldn’t (afford him).
“That has nothing to do with now. I know people are going to say ‘What is he talking about now, they are paying this player this or this player that’.
“At that time, when he left the club, we couldn’t. It was impossible.
“Of course, at that time you don’t know where he is going to go and you don’t expect him to go to Palace. That is his decision and his family’s decision, so fair enough.”