A goal from Gary Hooper and a brace from Paul Hayes earned the Iron a 3-0 friendly win at Blundell Park and Adkins is hoping to carry the momentum through the rest of pre-season.
"Yet again it was another good work out for us and we coped well with what Grimsby threw at us," he told his club's official website.
"We scored three good goals and Paul Hayes and Gary Hooper could have had more. We showed good promise going forward and it's all good.
"There are lots of things that we can take from the game, and we now move forward by going on our pre-season trip to Jersey."