That is what Tryndamere is good at. Tryndamere has one of the weakest solo lane phases in the game, and brings no poke or huge AoE to late game. All Tryndamere has is a BEASTLY auto attack, some mobility, and 5 second invulnerability.
If 5 seconds of auto attacking means you lose the game, you've basically already lost. And even so, you can CC him during his ultimate. Tryndamere cannot kill a Nexus from full hp while it's defended by 3 competent people.
Tryndamere is an AD CARRY. This could be done by any AD carry, it's what late game is all about. Once you aren't defended by turrets you should never leave your base without an inhibitor up.
Tristana could rocket jump over the wall and kill the Nexus
Graves could dash over the wall and kill the Nexus
Ezreal could blink over the wall and kill the Nexus
Corki could fly over the wall and kill the Nexus
Your team had no AD carry, that was a weakness in your composition and they abused the fact that if a base trade occurred that the could kill your buildings much faster. This is a reasonable strategy.