Upgrades (ie paying credits for levels) can only bring a capital ship to level 4 (with Basic Crew Training researched), combat experience is the only method for experience past that.
Basic Crew Training is Tier 6 Civilian for TEC, Tier 4 Hostility for Advent, and Tier 3 Warfare for Vasari.
The Advent actually have an easier time amassing experienced capital ships if they can get Mass Transcendence researched (though from what I've read, getting to Tier 8 tech is next to impossible in multiplayer).
Or did you simply not notice your allies' capital ships gain combat experience?