"I thought we were unlucky because I thought we did enough to win the game," admitted Adams.
"I'm disappointed obviously to only get a point because I thought we'd seen the game out, but we didn't quite pull it off," he added.
"We're not showing the desire in both boxes - either attacking or defending - and if you haven't got that then you've got a problem."
"I thought we defended well as a unit," he said.
"I was pleased with the back four, (Neill) Collins and (Shane) Lowry were outstanding, really."
But Adams did question whether his side were of the required quality to operate at this level.
"There was nothing wrong with the spirit. Whether we were good enough is another matter," he explained.
Millwall chief Kenny Jackett questioned the penalty decision which saw his side go behind, but the result was another indication of the progress being made by his players.
"It certainly shows how far we've come as a club when we're disappointed to come to Sheffield United and get a draw," he said.
"You should never be disappointed with a draw away from home. My first impression was that it looked a soft penalty, but I'll stand corrected if I think any different when I view the DVD."
Jackett added: "The one key decision was the penalty decision and the referee was backed up by his linesman.
"The goal came at a time when I thought we were making the running. As the game built up, we got on top. We finished very, very strongly, had a chance or two, and we could have won."