Kenny Clark's first-half goal was enough to condemn Town to defeat and cut their lead to fourth-placed Solihull to two points.
"I think it was a game of two halves, I thought they were far better than us first-half, played some really good stuff and caused us problems," Wild said.
"Too many of our players were off it, five or six of our players were below par, poor.
"We made our feelings known at half-time, and told them it wasn't good enough.
"Second-half I thought we had a right go, all the play was in their half but unfortunately we haven't broken them down.
"Ultimately, something we've been excellent at this year, the last two goals we've conceded have been from set-pieces, which infuriates me."
Wild admitted Southend's goal was very avoidable.
"You've got to track your men at set-pieces, got to stop them driving in the box, and we haven't done," he said.
"It's a really poor goal to concede."
When asked why Town were so poor in the first-half, Wild said: "Seasons ebb and flow, winning on the road's tough, you've got overnights etc.
"I don't make excuses though, we just didn't start well and that's frustrating."
Wild added: "I thought a draw would have been a fair result, we didn't do enough to win the game but a draw would have been a fair result.
"I'm really frustrated we haven't got a draw."
Captain Niall Maher went off in the second-half with an injury.
Wild was tight-lipped about the nature of the injury, but said: "He made us aware at half-time that he was struggling, he tried to carry on but it got to a point where we had to change it."
Wild also had bad news about defender Tom Bradbury.
"He's fallen on his knee and he's going to be out for up to six weeks," said the Town boss.
Striker Matty Stenson came off the bench after being recalled from his loan at Kidderminster.
"We need two big centre-forwards in the building, he gives us different ways of playing," Wild said.
"They crowded Billy (Waters) out, which some teams do, some teams give him space and some don't.
"They crowded him out so we need to be able to play different ways, and Stenson gives us a chance to play a different way."