The Gaels committed four errors in the fourth inning which directly led to two runs. San Gabriel Mission (6-10, 4-0) capitalized on most of the miscues.
Ziomek said Leyva might return Friday for a league game against Alverno and Ardines could return next week. The Gaels sorely missed both.
"The mistakes we made killed us," Ziomek said. "It's no excuse and these are plays that needed to be made.
"We see this as ourselves beating ourselves. Our confidence didn't break and we have to clean those miscues up."
Holy Family, which opened league with victories against L.A. Sacred Heart of Jesus and Bishop Conaty-Loretto, left the bases loaded twice. The Gaels loaded the bases in the second and seventh and came away empty.
San Gabriel Mission took a 1-0 lead against Holy Family starting pitcher Rachel Turner in the first. A groundout by Amanda Garcia brought home Priscilla Hernandez, who led off with a walk before stealing second and moving to third on a grounder.
The Gaels loaded the bases with one out in the second, but couldn't convert. However, Holy Family tied the game at 1 in the third on an error by the San Gabriel Mission shortstop that scored Elena Lomeli, who began the inning with a single and then stole second.
The Pioneers then took advantage of some sloppy defense turned in by the Gaels, who qualified for the playoffs last season. With one out, Garcia singled to left and moved to second on a throwing error by the left fielder. The Holy Family first baseman tried to throw out Garcia at second, but the throw went back into left field and Garcia scored to make it 2-1.
Nicole Holguin of San Gabriel Mission then singled to left and moved to second on a fielding error. She moved to third with one out on a wild pitch and scored on a fielding error by the Holy Family right fielder.
San Gabriel Mission Coach Jaime Preciado said he wanted the Pioneers to be aggressive when on base.