"We've dominated the game from start to finish, we've dominated the ball, we've had chance after chance after chance," said Wild.
"We just unfortunately have maybe been a bit naive out of possession trying to get that second goal, and maybe we should have shut up shop a bit more.
"But they threw three centre-forwards on to try and get something out of the game, they've got nothing to play for, so why wouldn't they?
"Unfortunately it's cost us late on today."
Wild added: "Both halves we've had lots and lots of chances to win the football match, and we haven't taken those chances, that's ultimately what's cost us three points.
"But we have to still remember that there's bumps in the road. I'm sure there's another twist and turn to go, and we've just got to keep going.
"We haven't lost the game, it's another point on the board and we keep going."
On Aldershot's equaliser, Wild said: "It is but they're leaving five up at that point and slinging it on us.
"So it's easy to say avoidable but at the end of the day when teams having to play for, they'll just gamble. They've gambled and it's come off for them, fair play to them."
The draw leaves it out of Town's hands whether they finish in the top three going into the final day of the season.
"I'm gutted, the players in there, they're all gutted, because it's a game we want to be winning," Wild said.
"We wanted to be in control of what goes on going into next week, but we're not.
"So we've just got to crack on and it makes next Sunday's game even better for the neutral because we've got to go there and take it to Stockport, so fantastic, what a great day that could be."
Asked how he now assessed the race for third, with Solihull enjoying a better goal difference by six, Wild said: "We'll just go and play the next game and see what happens."
But Wild stressed that any disappointment shouldn't obscure how well Town have done this season.
"It doesn't obscure anything, we've got 84 points after 43 games, it's unbelievable," he said.
"We all would have liked to have finished the job off properly, but we haven't and that's life and you move on."
On midfielder Kieran Green, who went off injured in the first-half, Wild said: "He's landed on his knee in a challenge, he tried to carry on but he couldn't, so we'll assess that over the next couple of days and see where he's at."
Wild says defender Jack Senior is 50-50 to be fit for next Sunday's game at Stockport.
"Jack tweaked his groin in training yesterday and couldn't go through the motion of passing the ball."
And on captain Niall Maher, Wild said: "He should be fit for next Sunday, and Tom Bradbury's 50-50."