No, this Huff Post article* which repeats the claim was corrected to say that it considers only University of California system:
Correction: [...] Language has also been amended to indicate that the article is considering the University of California system, and not the California State University system.
The University of California system indeed opened only one new campus since 1980, UC Merced, which started working in 2003-2004:
Faculty members began to arrive in 2003 with graduate students in tow and began setting up research laboratories and programs at UC Merced's ancillary research facility on the former Castle Air Force Base, biding their time until buildings were ready on campus. The first graduate courses began in fall 2004.
But, the California State University program opened another 3 universities in that time:
1989: Governor George Deukmejian signs Senate Bill 365 into law. The bill officially reconstitutes the SDSU satellite campus as California State University San Marcos — the first comprehensive U.S. university to be founded in two decades, and the 20th campus in the CSU system. Bill W. Stacy is named the university’s first president and is tasked with recruiting 12 founding faculty members.
Founded in 1994 on the former site of Fort Ord by educators and community leaders, Cal State Monterey Bay faculty and staff build on that legacy as we explore innovative ways to meet the needs of a new generation of students while simultaneously powering the Monterey County economy.
Established in 2002, we’re the youngest of 23 campuses in the CSU family.
During that time at 7 new community colleges were opened in California:
Clovis Community College was originally opened as a center in 2007, with the 80,000 square foot Academic Center One complex
Folsom Lake College was established in 2004 as the fourth campus of the Los Rios Community College District
Irvine Valley College, established in 1985 in Irvine
The Moreno Valley and Norco Campuses, opened in March 1991, have grown rapidly and were granted initial accreditation in January 2010
Norco College opened to students in 1991
Santiago Canyon College (SCC), established in 1985
West Hills College Lemoore was established in 2002
There are some community colleges which were opened before 1980, but became part of the California Community Colleges system after 1980.
In addition, according to the List of colleges and universities in California wikipedia page 37 private institutions opened since 1980 (of those two have been since closed and one is unaccredited).
* - The original claim seems to come from Business Insider, but appears withwithout any correction or clarification, see here (dated Jun. 13, 2012) and here (dated Apr. 12, 2012)