The Wire trailed from the eighth minute at the Halliwell Jones Stadium on Saturday but a 79th-minute try from Tom Lineham secured a fourth successive win for Warrington as they look to push into the top eight.
Smith accepts it wasn't a vintage performance from last season's runners-up but he says they are improving and was delighted they showed the strength to comeback and claim a victory.
“Our character isn't in question at all. Some of our processes are but our players are trying hard,” Smith told the Warrington Guardian.
"There were a few errors when they're getting up to play the ball. We need to get that right because it's hurting us.
"It comes from trying to play it quick but we showed great character. We felt if we held the lion's share of the ball, we would score points.
"Wakefield are dangerous and a good attacking team, they showed that. We never lost doubt about the result of the game but I'd like us to have taken a little more control.
"I felt for Wakefield by the end but we should have been in front earlier.We told the boys at half time to take more care but we made a mistake in our first set.
"That was a fourth game in two weeks for some of them. I can't be too critical of them.”
He added: “I'd love to say it was a brilliant game but I've got players out there that probably should have come off but they kept going.
"We'll roll our sleeves up because we've another game coming up.”
Warrington are next in action on Friday when they travel to Hull FC.