Adkins kept his players in the dressing room for 30 minutes after the game to discuss their poor display and has demanded an improvement for this weekend's FA Cup second round tie against Alfreton Town.
He said: "We let ourselves down. The performance wasn't good enough. It was all very disappointing. We were very poor, but all credit to Tranmere who battled really well.
"We never passed the ball well in the first half. We started off much better after the break, but their keeper made two fantastic saves. Then, when we hit a post in the 76th minute, we realised it wasn't going to be our night.
"We've had a good discussion about different things and I'm sure we'll be better next time. We have a group of honest professionals and know we're far better than we showed."