The winger had looked certain to leave Southampton for pastures new earlier this year after a public falling out on Twitter with chairman Nicola Cortese.
However, the pair - rather surprisingly - patched things up and, having helped Saints secure automatic promotion from the Championship, Puncheon is thriving in the top flight.
"I thought he had another excellent performance," Adkins said.
"He probably had a more consistent, complete game over the 90 minutes. He has done it in flashes.
"He has had a great pre-season and he has worked really hard. His attitude has been top draw and his performances has backed that up.
"He wants to have a go. Sometimes he has been in, sometimes he has been out. He could have scored more goals as he put several good shots in."