Teinaki led his team to a score of 121/8 in the first game which was not enough to chase down Rotorua's earlier score of 151/5, which saw the visitors drop too many catches.
Rotorua's top players in the match included Ryan Pedley who scored 50 not out and Tahir Afridi who took three wickets for three runs.
In the second match, Cook Islands batted first and posted an improved score of 144/7.
Rotorua then chased down the score with five balls to spare and seven wickets down. Ben Blackett top scored for Rotorua with 34. The Cook Islands visited the city as a warm-up to their T20 World Cup qualifiers near Brisbane.
The team left for Australia today and will spend two weeks in Lismore playing against other nations like Papua New Guinea, Vanuatu, Japan, Samoa, Fiji, Philippines and New Caledonia. The Cook Islands will need to finish in the top two at the tournament to progress to the next stage of qualifying.
Cook Islands captain Tino Etita said the trip to Rotorua and Australia would give their players really good experience to grow the game back home.
"Our cricket back home is just starting to take off," he said. "We have a lot of young guys with us who can take what they have learned here to other cricketers back home."
He said the majority of the Cook Islands team were based in Rarotonga.
The Cook Islands team was also scheduled to play a match against a Rotorua reserve side on Saturday, but the match was rained off.
The Rotorua representative side was made up of the best club cricketers in the area.
Results from the two T20 matches yesterday:
Game one: Rotorua 151/5 (Ryan Pedley 50no, Tahir Afridi 41; P Zekaria 2/40) defeated Cook Islands 121/8 (Toala Teinaki 60; Tahir Afridi 3/3, Ben Blackett 2/18)
Game two: Cook Islands 144/7 (T Vailoa 28, M Emile 27; Ben Blackett 2/8) lost to Rotorua 145/7 (Ben Blackett 34, Mehul Chaagan 31; T Etita 2/19).
