The Tech Room gives the impression that, without the Lucifer, the Shivans were uncoordinated and started to act...well, crazily. But Silent Threat seems to say otherwise, particularly in "Hellfire".
What happened, then, would seem to be equivalent to what happens to a human force when their command, control, and communications center is blown to Kingdom Come. There's confusion, people get bad information, seperate units can't coordinate, nobody knows what anyone else is doing. There's a tendancy to feel lost and alone, to retreat, scatter. Everything pretty much falls apart. Eventually someone reestablishes control, gets in touch with everybody, and things start working again...if you aren't destroyed before then.
When the Lucifer went kablooie, the Shivans lost their primary C3 center. All of the above happened, compounded by the GTA and PVN going on the offensive and adding even more confusion to the situation. Eventually (a week, two weeks?) the secondary Shivan commanders, whoever they might be, reestablished control and got the fleet together again. (Hence "Hellfire".) But by that time it was too late. The GTA and PVN had already done too much damage to the Shivans, and they no longer had the firepower left to win.