Stefano Eranio scored the only goal from the penalty spot after 42 minutes but Smith singled out Poom as his man of the match. The 25-year-old Estonian international made a number of fine stops, including a double save from Andy Liddell, and Smith said: "The best two players on the pitch were the goalkeepers.
"Mart is going to be a very, very good keeper and this will have been a great boost for him. He has a lot to prove to himself. This week we have been working on his composure and I thought he stood up well and made some great saves."
Derby had to twice take their penalty, awarded when goalkeeper Lars Leese pulled down Francesco Baiano, because referee Paul Durkin ruled that Leese had stepped off his line after Eranio had scored when Baiano's initial kick was saved.
Smith revealed that after Baiano - signed for pounds 1.5m from Fiorentina - had missed, Eranio opted to take over the responsibility. "Eranio was our selected penalty kicker but Baiano wanted to take it. After he missed Eranio took it upon himself for the second attempt," said Smith.
The Derby manager was impressed with Baiano on his debut and felt he and Dean Sturridge would form a formidable partnership when they are both fully fit. "We now have a fortnight before our next game and we will be working on getting both of them match fit with reserve games."
Barnsley's manager Danny Wilson felt his side had been handed another painful lesson in life in the fast lane of the Premiership. He felt they were worth a point but admitted they cannot afford to miss chances at this level.
"I though we played very well in the second half and it was one-way traffic," he said. "We had three to four clear-cut chances which we did not take advantage of, and if you squander that type of chance you will be punished. That's the harsh reality of the Premiership. I'm sure there are more harsh realities awaiting us in the future.
"We have started OK apart from the hammering we had against Chelsea. The other games have been OK - so there are a few positive things we can take."
Goal: Eranio (pen 43) 1-0.
Derby County: Poom; Powell, Stimac (Trollope, 73), Van der Laan, Ward, Laursen, Carsley, Eranio (Rowett, 53), Dailly, Hunt, Baiano (Sturridge, 77). Substitutes not used: Asanovic, Hoult (gk).
Barnsley: Leese; Eaden, Appleby, Moses, De Zeeuw, Redfearn, Marcelle (Hendrie, 57), Liddell, Tinkler, Hristov (Wilkinson, 61), Barnard (Sheridan, 34). Substitutes not used: M Bullock, T Bullock.
Referee: P Durkin (Portland). Bookings Derby: Eranio, Dailly, Laursen. Barnsley: Sheridan, Appleby.
Man of the match: Poom.
Attendance: 27,232.Reuse content