Adkins said the incident occurred after Lambert equalised during the dramatic finale to Saints' 3-2 win against Millwall at The Den.
The Daily Echo understands fitness coach Nick Harvey was the person struck.
Adkins said: “One of our members of staff sat on the bench was all of a sudden pelted with numerous objects and had to have a couple of stitches in his forehead.
“It’s not right for me to name names but it was an important member of our staff and I’ve got photographs with blood streaming down his face.
“It was an unsavoury moment. A lot of objects got thrown in the dug out, it was pelted with all sorts."
More Nigel Adkins reaction to today's win in tomorrow's Sports Pink