Three Kings are roughly three divisions higher than Ngongotaha and play in the highest tier of club football in Auckland.
"I'm very proud of the effort our guys put in today," Davis said.
"We matched them with everything, we actually gave them a really big fright."
He said Three Kings' fitness was the only difference in the end as they pulled away in extra time.
The Chatham Cup is New Zealand's premier knockout competition and is open to all senior football clubs across the country.
Only one Bay of Plenty club still remain in the knockout competition, Tauranga City, who defeated University of Auckland 2-0 yesterday.
Meanwhile, in the WaiBOP Premiership on Saturday, Rotorua United managed to string back-to-back wins together.
United's improvement in the premiership continued with a 2-0 home victory over Matamata Swifts, which also saw them defend the Federation Challenge Shield.
A goal in each half from Brad Hill and Lawrie Scott got the job done for United who ease themselves further away from relegation problems.
Cambridge reinforced their favourites tag for the 2015 WaiBOP Premiership title after dismantling SGS Papamoa 4-1 at John Kerkhof Park on Saturday.
Glen Carmichael led the way for Cambridge with a well taken double.
In other premiership matches, Melville United moved into second on the table with a comfortable 2-0 home victory over unpredictable Old Blues.
Katikati heaped further pressure on Otumoetai with a 2-1 victory while the bottom sides, Tauranga Boys College and Tauranga City United, fought out a 2-2 draw.
- WaiBOP Football results Saturday:
Premiership: Melville United 2-0 Tauranga Old Blues, Cambridge 4-1 Papamoa, Katikati 2-1 Otumoetai, Rotorua United 2-0 Matamata, Tauranga Boys' College 2-2 Tauranga City United, Ngongotaha v Waikato Unicol - postponed.
Championship: Cambridge 2-0 Te Awamutu, Claudelands 4-2 Matamata, Whakatane Town 0-2 West Hamilton, Kawerau Sports 5-0 Ngongotaha, Te Puke v Tokoroa - postponed, Tauranga Old Blues bye.