Hermann Hreidarsson's 24th-minute strike, his first goal since 2009, secured Pompey a sixth straight win which keeps their slim play-off hopes alive.
The beleaguered Blades, however, remain in the Championship relegation zone six points from safety.
Adams said: "Nicked a point? I think that was the least we deserved, but once again it's a fine line between success and failure. We've seen that again.
"We conceded a goal from a corner and for long periods of the game we had Portsmouth pinned back without it falling for us.
It seems to be the story of our season. We conceded another goal from a set-piece, which is obviously our Achilles heel. Then we attacked, but it has just not fallen for us in the box. We got into some great areas without really testing their goalkeeper. But we're not down - we'll keep going."
Source: PA
Source: PA