Staunton, one of three full internationals in the starting XV, expressed his personal satisfaction afterwards, having played for the first time in two months after his recovery from a thumb injury.
"It was great to just get back on the pitch and play again having had about eight weeks out," Staunton told reporters at Exeter's Sandy Park.
"I thought we played well for the majority and have gelled really well in the short time we have been together.
"There were some scrappy phases which we must work on before we play the New Zealand Maori, who will be extremely tough opponents.
"We have 10 days to prepare for that match and will work on all aspects of our game."
Staunton was due to jet out to Argentina at the weekend for the senior squad's summer tour, but coach Eddie O'Sullivan decided to put the Limerick man on Churchill Cup duty as game-time at the tournament should improve the 27-year-old's chances of a World Cup slot.
Staunton's fourth and most recent Ireland cap came against Australia last June.