New Zealand international James scored in the game, but Adkins feels he is not strong enough for first-team football.
"Unfortunately I think he's a little bit lightweight," Adkins told BBC Radio Humberside.
"He's done alright, but physically he needs a bit more about him."
Marr is a free agent having been released by Newcastle, but is not likely to be offered a contract.
Cameroon U-22 international Mowfor impressed in pre-season friendlies against Chesterfield and Lincoln, but suffered an ankle injury against the Imps.
He is currently in France receiving treatment on the injury, but it is not as bad as first feared and Adkins expects him to return to North Lincolnshire.
"We are in discussions about bringing him back to the club," added Adkins.
"He's ahead of the average 19-year-old, he's got a bit of flair about him, I'd like to bring him here but there are a lot of discussions ahead."