A money-spinning final at Wembley would have determined who won a place among Europe's football elite but the proposals have been rejected by the Premier League following a vote among its 20 members.
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"More chairmen wanted to introduce it than those who didn't but the rules state that such a decision must have a two-to-one margin in favour and we didn't have that.
"There were a lot if reasons for and against introducing such a system and certainly more pros than cons for Sunderland so I voted in favour."
Quinn continued: "The big four naturally were uncomfortable with the thought of losing one of those coveted spots that they have pretty much carved up between them in the past. This was the opportunity to open it up a little but that chance has gone now.
"The subject was discussed thoroughly and fairly and I accepted the decision but who knows it could have been really good."
Quinn and club owner Ellis Short can now look forward optimistically after manager Steve Bruce guided his team to their first Premier League win since November with a 4-0 victory over Bolton that eased relegation fears at the Stadium of Light.
It marked a return to the early-season form that suggested Sunderland might compete for European football this season but Quinn is determined that the club will not over-stretch itself.
"The interest in the Premier League from overseas remains phenomenal and it continues to go from strength to strength," Quinn added.
"That said we are mindful of the challenges that lie ahead in the light of the situation Portsmouth find themselves in. As the guardian of the club I must look hard at our financial model."