Panich, a Glendale High graduate, shot a seven-over-par 72 on Monday to place third behind Dee Ray of Bakersfield (72) and Taylor Gould of College of the Canyons (76).
Panich, a former All-Area member, finished with two birdies despite her illness.
"I thought that she would tear this course apart," Glendale college first-year Coach Greg Osbourne said. "She was just off and there was something wrong because she was sick over the weekend.
"She and the team did the best they could."
Canyons won the event with a 321, followed by Bakersfield (331), Santa Barbara (347), Citrus (no score reported) and Glendale (258).
Diana Hernandez shot an 89 for the Vaqueros, who also received a 90 from Imelda Treto.
Glendale competed without Louise Wright, who missed the match because of a previous engagement.
The Vaqueros will next participate in the two-day conference championship, which will be held Sunday and Monday at Olivas Links Golf Course in Ventura.
Canyons has already locked up the conference championship and has punched its ticket to the Southern California Regionals, which will be held in Solvang in November. Osbourne said the Vaqueros are looking to grab the second and final spot from the conference to advance and have Panich, who earned medalist honors during a conference match Oct. 18 in the Santa Clarita Valley, capture the conference's individual championship.
"Next week will be the most important for Tammy," Osbourne said. "She'll try to prove herself all over again.
"It's possible that we can get the lowest 36-hole next week to get to regionals. It's possible because we'll have four players this time, so we actually do have a chance."