Gooding was dismissed for 18 in the eighth over and Tallott (21) departed two balls later.
From there, the Bay lost a further six wickets and struggled for runs to finish at 79-8.
In their second game yesterday, the Bay faced Waikato Valley, a team they had expectations of beating.
Batting first, they lost Gooding with only two runs on the board.
A second-wicket partnership of 102 between skipper Danny Gibbs and Craig Christophers revived the innings.
Gibbs scored 62 off 43 balls including seven fours. Christophers hit 39 off 45 balls when he was dismissed. Gibbs followed one run later.
From 105-2, the Bay limped to 126-6 in their 20 overs.
Waikato Valley were in trouble at 64-5, with Gooding and Richard Mills each taking two wickets.
However a sixth-wicket stand of 63 carried Valley to their target with three overs remaining.