It was only the Blades' second league match since December 4, their first this side of Christmas but eight of the starters also kicked off an FA Cup tie at Wolverhampton Wanderers six days earlier, and two came off the bench.
The Blades were sloppy in possession and looked short of confidence in a game which apart from Lawrence's two second-half goals was of low quality.
"Without them it might have petered out to a 0-0," said McCall, who was in charge on the day because Paul Heckingbottom was isolating at home after testing positive for Covid-19 at the start of the week. "(In the) second half we had more possession, more of the ball, but didn't do anything with it.
"It was 61 per cent possession in the first half but we just didn't do enough with ours.
"We got into wide areas and the ball hit the first man. Credit to them, they defended well, got back in numbers.
"We weren't bright enough in and around their box, which we've worked on all week but you give the opposition credit for giving bodies in there.
"We can't look at other clubs, we've got to look at ourselves. We didn't do enough. We can point out how our keeper's not had a save to make, they've had two shots on goals and scored them both with two bits of brilliance."
Of the goals, McCall said: "We mentioned at half-time the only way they're going to hit us is on the counter-attack. We just make a change in shape and we don't get the press right from the goalkick. It's the little details that can hurt you.
"We've been popped off and to be fair they still had a lot of work to do. He's danced by a couple of our defenders and we've got to defend better, there's no doubt about that.
"From his point of view it was a terrific individual goal. From our point of view it was poor defending.
"The second goal, we've got to win the ball on the edge of the 18-yard box, the kid (Festy Ebosele) breaks, we all know abut him, and he carries the ball well but just like we said with )(Adama) Traore last week at Wolves, if he's on a run we've got to bring him down, it's game management, you've got to take a booking.
"It was a fantastic finish by the boy (Lawrence) in the top corner."
Asked what part his team's inactivity played, McCall said: "It's okay for other people to say that because if we say it, it is an excuse and we don't want to give the players or ourselves any excuse whatsoever. The momentum was halted a little bit after the win at Fulham.
"If we were a little bit rusty we can't be rusty on Tuesday night. There's no excuse on Tuesday night.
"That's your one opportunity now. There's no excuses, 100 per cent on Tuesday night to not go in and put in a totally committed performance."
Heckingbottom is hoping to be back at work for Tuesday's game at Preston North End.
Derby manager Wayne Rooney, who saw his team move above Barnsley and off the bottom of the table for the first time since the first of their two points deductions, said his team had made a good side look "ordinary".
"I always felt in control and I said at half-time we would win this game," he said.
“Since the change of manager they’ve been In good form and we knew it was going to be difficult.
“The manager and coaches are doing a fantastic job there but we took away their qualities, made them go a bit more direct and battled against them.
“We felt that was the best way to win the game. I think they have a chance of making the play-offs. They have some very good players and if they keep showing the form they have done they’ve got a very good chance.”