The governor's proposal, released last week, awarded the UC system an additional $142.2 million from the General Fund in 2014-15, a 5 percent increase from last fiscal year.
Meeting with The Sacramento Bee's Editorial Board, Napolitano did not explicitly call for more funds, but said: "We'll have a discussion about what else can the university do and what other needs that we have."
"We all know state funding had to get slashed (during the recession). I can appreciate the difficult decisions that had to be made," she added. "But we've leveled off now."
Napolitano, a former Arizona governor and Secretary of the U.S. Department of Homeland Security who assumed the office of UC president in September, was in Sacramento Wednesday for meetings, including a noontime gathering with legislators.
During her hour-long discussion with The Bee, Napolitano touched several times on Gov. Brown's budget, which also ties funding increases for UC and CSU to tuition freezes and creates a $50 million "innovation grant" program to develop ways to get more students graduated with degrees faster.
With California's public universities expected to maintain their current fee levels through 2016-17, Napolitano said her focus will shift to guarding against future tuition volatility. The UC has previously seen massive spikes in tuition after extended freezes -- such as a 40 percent jump from 2002 to 2004 following nearly a decade of freezes and reductions.
Napolitano said she didn't expect to roll back any of the most recent tuition hikes "unless the state substantially increases the amount it puts into the university -- and I don't foresee that."
Among Napolitano's pitches for the innovation grant was an interactive database that she is developing with the CSU and community college chancellors to track community college students who are interested in transferring to four-year schools. The database would help guide students' study plans to smooth their transition to the UC or CSU systems.
She was more skeptical about massive open online courses, which have been a favorite of Brown's.
"The idea that you can just have an online course and that's gonna solve all your problems and cut your costs...that's no silver bullet," Napolitano said. "But it is a tool."
UC is currently experimenting with a few online programs to augment its educational mission, she said, such as a pilot slate of multi-campus classes for the spring that would allow students to take some required courses not offered at their campus remotely.
Next, Napolitano heads to Washington, D.C., where she will meet Thursday with President Obama and other university leaders from across the country to discuss improving college access for low-income students.
Napolitano has publicly expressed doubt about her former boss' plan to develop a scorecard measuring the value of colleges. She told The Bee Wednesday that federal government's role in higher education should primarily be to provide research funding, of which the University of California receives about $4 billion per year.
PHOTO: New UC President Janet Napolitano meets with editorial board at the Sacramento Bee on Wednesday, January 15, 2014. The Sacramento Bee/Hector Amezcua