After fighting back for points against Leeds and then Tottenham, they were ready for their 10-day break, Smith said. Unfortunately, one or two of them seemed, in their minds, to have their feet up in front of the telly already. And those who had been asked, one assumes, to attack the Villa goal once in a while did not appear especially keen to do so.
With Dean Sturridge having joined Ashley Ward on the injured list, Smith's options were limited yet he chose to leave the bustling Marco Gabbiadini on the bench while apparently detailing Aljosa Asanovic, his Croat midfield player, to support Ron Willems up front.
Asanovic's instincts are clearly to sit back, which he generally did, while Willems was inclined to drift wide. As a consequence, Derby's attacks tended to reach the edge of the penalty area and then go sideways. Apart from the odd long-range shot, two of which he pushed out for corners rather untidily, Michael Oakes had barely a save to make.
This was a pity because in Darryl Powell, a hard worker in the anchor role, Asanovic and Christian Dailly, Smith had three players in midfield capable of winning the match, even up against the combined talents of Villa's central trio, in which Brian Little teamed Mark Draper and Andy Townsend with the impressive Sasa Curcic, his pounds 4m acquisition from Bolton, whose work permit arrived last Friday.
Not that Villa were much better off in attack. Savo Milosevic is still unfit and Dwight Yorke left with a pulled hamstring after 14 minutes, an injury for which 10 days may not be enough.
However, in Yorke's place Little sent on Julian Joachim, the pacy former England Youth player of Robbie Fowler's generation. Tommy Johnson made his mark in characteristic fashion, hitting the woodwork at the end of the first half and winning the penalty at the start of the second, which he converted himself. But it was Joachim who was Villa's edge.
He took his goal well, stretching out a leg to whip the ball home as Russell Hoult rushed out to meet him, but failed to capitalise on better opportunities later, when more composure was needed. He is not the player Fowler has become but time is still on his side.
Goals: Joachim (19) 1-0; Johnson (pen 46) 2-0.
Aston Villa (5-3-2): Oakes; Taylor, Ehiogu, Southgate, Staunton, Wright; Curcic (Nelson, 80), Draper, Townsend; Yorke (Joachim, 14), Johnson. Substitutes not used: McGrath, Scimeca, Rachel (gk).
Derby County (5-3-1-1): Hoult; Laursen, Parker, Stimac, Rowett (Van der Laan, 16; Gabbiadini, 57), C Powell; Dailly, D Powell, Flynn; Asanovic; Willems (Simpson, 74). Substitutes not used: Taylor (gk), Carsley.
Referee: P Alcock (Redhill).
Bookings: Derby: Parker, Stimac.
Man of the match: Curcic (Villa). Attendance: 34,646.