Padiham, who had midfielder Michael Morrison sent off in the first half, had led with five minutes to go thanks to Spencer Jordan’s debut strike, but Hanley Town hit back twice late on.
“We were nowhere near good enough in the first half,” said the club’s joint manager. “Collectively we were miles off, which was disappointing.
“It’s always going to be difficult with 10 men, but they responded after the break and did everything that we asked of them.
“Unfortunately we were punished from little lapses of concentration, but it’s physically and mentally draining playing with a man less.
“On another day we would’ve won the game – Danny Boyle strikes the ball almost too well and it hits the bar.
“It’s unfortunate but I can’t question the performance, commitment or desire. We will take it on the chin, work hard to get a reaction and put things right.”
Padiham, though, have character and they have it in abundance at the Ruby Civil Arena.
It was tested following the 6-1 hammering away at Runcorn Linnets on Smith’s managerial bow and it will be evaluated once more when they take on AFC Liverpool at the Marine Travel Arena on Saturday.
Ahead of the Hallmark Security Premier Division clash, Smith said: “The lads have been great. They know they weren’t good enough.
“We are an honest group. There were a couple of things that we got wrong as a management team too, and we’ll hold our hands up.
“We watched AFC Liverpool last week so we know what they’re about. We’re confident that we can devise a game plan that will secure us a positive result.
“They are a young side and we saw them against Barnoldswick. We’ve had a couple of reports back about them since.
“We’re confident of beating them, but we know it will be tough. It’s always difficult going to play any team in Merseyside. We’ll match their work rate and desire and hopefully our quality will shine through.
“I’m backing them 100% to bounce back at the first opportunity. They’re experienced enough at this level to know what it takes to be successful. Everyone one of us in that dressing room knows what it takes.
“There are some great characters in the dressing room and they will do everything they can to put things right. This will be a good test of character.”