Lambert was ruled out of the Bloomfield Road encounter with a pelvic injury suffered in the 2-0 win over Doncaster last weekend and watched on as the Saints saw their lead at the top of the table cut to two points.
Adkins told BBC Radio Solent: "Rickie Lambert does not need an operation, he has not had an operation.
"We thought he was going to be fine for Saturday but he wasn't. He trained Thursday, did half the session, came off and was very uncomfortable.
"The last thing we want to do is lose Rickie Lambert for a long period of time. We have other strikers here who are fit so we utilised them."
Southampton face relegation threatened Portsmouth in the south-coast derby at St Mary's at the weekend.