The Saints lost 3-2 to the Premier League champions on their return to the top flight and at one stage led 2-1.
Lambert, who was the Championship's top scorer last season, equalised for Southampton just four minutes after being brought onto the field as a second-half substitute, however Adkins says that leaving the 30-year-old out of the starting lineup was a tactical decision.
"It was a big decision to leave Rickie out but I've got to be brave enough to make them," said Adkins.
"We got him on the pitch in the latter stages of the game when he's going to be dangerous and what a great goal it was. That's important.
"We ran them close but our endeavour is to win. We've got to find ways to win."
Saints host Wigan Athletic in their next Premier League match.