There were two reasons.
The Lakers will be in town Wednesday night. And he remembers what happened last season.
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"We were here last year and let it go," Jefferson said of a 15-5 start that ended with Utah missing the playoffs.
"That's why I'm not as excited. We play every game like we're last in the West and that's what we are going to continue to do until all is said and done. Everybody's got to keep that same attitude. We got to stay hungry."
It won't be hard to get up for the Lakers.
Kobe Bryant and the rest of the Lakers handed the Jazz a 96-71 thrashing in Utah's opener Dec. 27, even with Andrew Bynum suspended.
"It was embarrassing to get beat like that," Jefferson said.
"We are a better team than the first time we played them, but we still got to come because they're a great team and will be ready to play."
It should help that the Jazz (6-3) are playing at home, where they are 5-0 this season - their best start at home since beginning the 2008-09 season at 6-0.
After losing their first two, the Jazz have found their rhythm. And it starts with their big men.
Jefferson finished 13 of 17, with 12 rebounds and two blocks.
Strong forward Paul Millsap started 9 of 9 shooting and finished 9 of 10, with 19 points. And second-year pro Derrick Favors added 14 points off the bench.
Combined they were 27 of 33 for 63 points, as Utah scored 56 points in the paint.
"He was on a roll toward something very special tonight," Jefferson said of Millsap. "When he got in foul trouble, that's when I had to step up and pick it up on the offensive end."
In the third, the Cavs opened on a 13-7 run, with Antawn Jamison scoring 13 in the period. But Jefferson scored 14, and each time Cleveland made a move, Jefferson countered.
Cleveland pulled within six points midway through the fourth quarter before Josh Howard converted a three-point play. Jefferson then added a pair of jumpers, and C.J. Miles hit a late 3 to seal the win.
Rookie Kyrie Irving added 20 points for the Cavs (4-5), who fell to 1-3 on a seven-game road trip, and visit Phoenix, the L.A. Lakers and Charlotte next.
"It's difficult to have one of those guys feeling it throughout the game, but to have both of them start out the way they did really put pressure on our front court," said Jamison, who finished with 22 points and seven rebounds.
"They had us in scrambling mode all night. They got into a rhythm at both ends. Jefferson was able to [sustain] it through the four quarters. It makes a difference."
Such an inside presence opened things up outside for guys such as Howard, who added 17 points off the bench, including the critical three-point play after the Cavs had cut the gap to six points, 91-85.
Howard, Utah's biggest free-agent acquisition, grabbed an offensive rebound and headed for the hoop. Tristan Thompson was called for goaltending, and Alonzo Gee the personal foul.
"I knew it was going up, but didn't actually see where it was going up," Howard said. "Fortunately I got the call and knocked down the free throw."
The Cavs made another push behind Irving, whose driving jumper pulled Cleveland within 106-101 with 57 seconds remaining.
But Miles, who had played only 13 minutes combined in the previous two games and was shooting 30 percent overall, hit a 3-pointer with 36 seconds left to bump Utah's lead back to eight.
"Guys found each other [for open looks]," Millsap said of Utah's 59 percent shooting, including 61.5 percent in the first half.
"We set screens for each other. The ball was moving. We just did a great job on the offensive end moving the ball."
And Jefferson, who dropped 8 pounds since the start of training camp, kept scoring.
"It's the best I ever felt," said Jefferson, who spent all offseason and the lockout working out with specialty trainers in California.
"I like to have a little weight on me because when you're playing against a guy like Andrew Bynum, you've got to be able to be physical with them. But at the same time, I'm quick enough. I feel really good."
He knows not to get ahead of himself.
"We don't want to be a team that's known to play well the first half of the season," Jefferson said. "We want to be that team that stays consistent and is a playoff team. Right now we are, but we got a long way to go. We got to stay hungry. Coach treats us like we done lost six in a row, and that's what we need. It's a young team; that's what we need. We just got to keep rolling."
The wife of Utah guard Raja Bell gave birth to the couple's third son at 11:18 a.m. Tuesday. The boy weighed in at 4 pounds, 12 ounces. The couple has yet to announce a name. Bell started 0 of 2 and finished with six points. ... Jazz coach Tyrone Corbin has yet to select a captain. ... Cavs guard Irving entered the game averaging 15 points - most among rookies. ... The 113 points allowed by the Cavs are the most Cleveland has given up this season.