But their efforts proved in vain as New Zealand stole it 24-22 at the death with a converted Ryan Crotty try.
It would have been Ireland's first-ever victory over the All Blacks - who will host the next Lions Tour in 2017 - but Kearney insists his nation have emerged with their belief intact.
"When we tell you that when we play our best rugby we can beat any team in the world, that's not a party-line that we trot out, that's what we genuinely believe," he said.
"I haven't learned a huge amount from that 80 minutes - I know what we can do as a team when we fulfil our potential.
"I know we can beat the best teams in the world, and we came pretty close on Sunday.
"It enhances the next time we do play them - it will heighten our belief a bit more."