TEC are actually significantly worse off in Single Player as well, at least in a late game, big galaxy situation. It's not hard to extrapolate those problems into multiplayer, even though I don't partake and the problems aren't really the same. In 1v# comp games, both Vasari and Advent have hugely useful late game techs that facilitate a reasonable rate of victory.
Vasari have Phase Stabilizer Nodes, which trivializes defense and allows fleet consolidation because the AI don't prioritize them. Every planet you own is a choke point when they all have gates. Overseers shine in big fleet battles because of their direct heal and the AI's tendancy to attack capital ships, even when pointless. If you can stand the macro, RA and salvage spec is a better economy than TEC has by far, though I don't use RA myself. The Evacuator's gravity bomb is hugely useful in trapping fleets, and explosive nanites is hugely useful in wiping them with a chain reaction. Subverters, enough said.
Advent has a fleet superiority that mostly lies in its ridiculous capital ships. While people are already quite aware of Illuminators and Repulsion, there are several other key advantages Advent get against greater numbers. Malice and Cleansing Brilliance allow for a maddening rate of kills, Vengeance and Telekinetic Push essentially shut down all strike craft, and the Rapture aura for allied strike craft is just incredible for razing orbital structures. This race is a little tougher than Vasari to manage on a wide scale, but once you get the steps down it's a juggernaut.
TEC have... ? Novalith cannons I guess? The late econ tech involving recources for enemy production is good, but it's only good in a big game with several players. Dreadnaughts are about the only strong AE that the TEC have, and without the disables Vasari have to make up for it. TEC support cruisers have abilities that are too subtle for late game fleet battles. The capital ships are strong in direct combat, but not on a scale wide enough to deal with multiple foes. Armistice is good, but again the problem is in kill speed/efficiency, not survival. If you can't kill lots of ships quickly, they'll just warp away from superior fleets and stalemate you with hit and run. TEC is the only race that seems to need a choke point.
Yeah, TEC can win 1v1 just fine, but the AI is so weak in battles that TEC problems don't really start to shine through. You can also win against AI building only capital ships or zero capital ships, either of which is hugely underpowered all things considered. Multiplayer is much more competitive, and forces players to really analyze the potency of each race. I agree that TEC needs something beyond fixed Marza to be on the same level as the other two. Sadly, I'm still not versed enough in the game's nuances to suggest exactly what it is they need.