The Nets yesterday announced the signing of general manager Billy King to a multi-year contract extension, but if you think that enhances the chances of P.J. Carlesimo returning as the Nets head coach, think again.

King was all smiles during the Nets breakfast yesterday, while Carlesimo wore the frown of a head coach trying to figure how to end a two-game losing streak and beat the Bulls in Game 4 tonight at the United Center.

With the Nets down 2-1 in the best-of-seven series, Carlesimo stopped short of calling it “a must-win” game.

“Must-win games are elimination games,” he said.

But he did call it the most important game the Nets have played this season. And it’s the most important game for Carlesimo.

King has his job security, but the sense around the Nets is that Carlesimo has to take the Nets deep into the playoffs to have a chance to keep his job. The thinking is owner Mikhail Prokhorov wants a more high-profile coach. Jeff Van Gundy’s name continues to be prominently mentioned.

A quick exit against the Bulls almost certainly would end any chance of Carlesimo staying. Losing to Chicago in five or six games would be frustrating considering the Bulls are without Derrick Rose and Joakim Noah is hobbled by a foot injury.

After playing so well in Game 1, the Nets haven’t adjusted to the Bulls’ up-tick in defensive pressure. In losing two straight games, they have been a mess offensively, shooting 35 percent from the field and 21.4 percent from 3-point range.

Deron Williams, shooting 26 percent in his last two games, continues to get pushed to one side, preventing him from finding a rhythm as a scorer or penetrator. Brook Lopez scored 22 points in Game 3, but the prevailing image is of him missing several contested shots in the paint.