Dele Adebola gave the Reds the half-time lead at Bramall Lane but the Blades hit back to win 2-1 in the second half.
The defeat leaves Davies` side in sixth place, four points behind second-placed Swansea but three points ahead of seventh-placed Burnley, who have two games in hand.
"For 60 minutes I didn't see us in any trouble," said the Scot. "I thought first half we played better than the home side, I thought we had a couple of good chances, showed some good quality and scored our goal, we deserved to be in front.
"We needed to get the second goal, we didn't pass well enough in the second half, our positional game wasn't good enough, we played too direct and we didn't influence the game enough in the final third. For the last half-hour we looked mentally tired, that's the best way to describe it."
Davies added: "The target before this game was five or six points out of the next three matches, now we've got to take six points from the next two games."
Source: PA
Source: PA