Vale's early dominance was rewarded with Jennison Myrie-Williams' penalty but Boro woke from their slumber to score in their first two serious attacks shortly before half-time, Jordan Burrow bagging both for the visitors.
Adams said: "I'm pleased we've got something out of the game. We haven't drawn many this season and I thought our point was warranted.
"We started the game very well and our forward play was good for most of the game, but I'm afraid some of our defending was unacceptable.
"There is no doubt we will do a lot of defending sessions in training this week. For some strange reason we retreated further and further back and we didn't deal with Luke Freeman and Francois Zoko well at all.
"We got beaten too easily in one-on-one situations, but that has happened before with us.
"When we came in 2-1 down at half-time it was difficult to believe because we had dominated most of the play. But when we defend like that it makes things very difficult."