The result helps alleviate the pressure mounting on Adkins, whose future has come under increasing scrutiny in recent weeks.
Southampton have found themselves in the headlines for the wrong reasons as a result and Puncheon admits it has been hard to ignore.
"It's natural, we're human beings at the end of the day," he said.
"Just because we're professionals it doesn't mean that we don't see and hear things. We've got eyes and ears.
"That's part-and-parcel of football so you've got to take that on the chin and turn up on a Saturday."