Adkins felt his side had not reached the heights they had shown in the home win over Sheffield United but was happy to take a point against fellow strugglers Barnsley.
The Tigers boss felt his players had not started the game well but gave them credit for their response to going behind as they came back to claim a share of the spoils.
The Hull boss had seen his side dominate for long periods but go a goal behind in the first half when Oliver McBurnie rose unmarked on the edge of the six yard box to head a cross from Brad Potts into the top corner.
The Tigers worked hard in response but their forwards lacked a clinical finishing touch that central defender Michael Dawson showed with 17 minutes remaining when he shot home from the edge of the area after Barnsley failed to properly clear a corner.
Adkins said: ‘I respect the point because it’s important but there was a chance for us to get three. It’s another game undefeated at home. We will take that and we will get ready for the next game.
‘We just weren’t at the heights (we showed against Sheffield United) for whatever reason.’
Adkins bemoaned his side’s slow start which saw McBurnie score his third goal in two games.
He added: ‘It was a poor goal we gave away. We responded and Michael Dawson scored a good goal.’
Newcastle have been linked with a shock move for former Sunderland goalkeeper Simon Mignolet during the summer.