Mike Finger, the Birmingham coach, said: "I told the players I believe we have the best team in the league and now we must prove it by grabbing that last piece of silverware."
The Bullets won 67-65 at Wembley against London Towers but needed the Sharks to win to stop the Leopards from becoming the first team in six years to successfully defend the title.
Birmingham matched Leopards' record of 29 wins from 36 games, but the title stayed in London because the Bullets lost the head-to-head series by 2-1.
Finger said: "We lost control of our own destiny when Derby Storm beat us. That meant we had to win all our remaining games but still needed help from other teams."
On Sunday the Bullets- Towers game finished first and Finger and his players watched the closing stages from Sheffield on a television monitor.
"We all felt Leopards would do it. But when Sheffield had the ball in their hands, game tied, and six seconds to go, I started to wonder. It was a tease, but we can't worry about it now."
In the best-of-three play-off quarter-finals Bullets face Derby again with the first game at Moorways on Saturday. The four survivors play at Wembley arena on the first weekend in May.