Back-to-back wins over the Bank Holiday weekend against Yeovil and Eastleigh mean Halifax are still third with just two matches remaining.
Winning the league is still mathematically possible, but a second or third placed finish is more likely for Town, who are guaranteed to finish in the top four.
The Shaymen play Aldershot at home on Saturday and then leaders Stcokport away on Sunday, May 15, with fourth-placed Solihull at home to Dagenham and Redbridge this weekend before visiting Boreham Wood on the final day.
Wild said getting six points from their last two matches was vital for Town's hopes of a top three place.
"It's huge, massive, and it allows us to just keep going, stay ahead of the curve.
"That's all we've got to keep doing," he said.
"Nothing's done yet, we've got to keep going, go into Saturday and try to get the right result and hope Dagenham do us a favour against Solihull."
But Wild says Town supporters shouldn't be expecting a comfortable afternoon on Saturday against Aldershot, who are 20th in the table.
"Nothing's straightforward in football is it, if you think we've cracked and we're just going roll up and turn them over, not a chance," he said.
"They're going to come and give us a right game, and we've got to be ready for that.
"I know Mark (Moseley, Aldershot manager) well, he wanted to get them playing, wanted a good football side.
"They've had some excellent results recently, so it's another big game for us and one we've got to try and do well in."
It's been a season to forget for Aldershot, but they beat Boreham Wood, Yeovil and Notts County last month, showing they are not ready to sign off for the summer yet.
"You want to finish the season well, that's what I'd be saying, let's finish the season well, and I can see that in Aldershot, they're picking up results, which tells me that they've not given up yet," Wild said.
The Town boss feels Monday's 2-1 win at Eastleigh, coming just two days after the win against Yeovil, exemplified just how much his side want that coveted top three place, which would give Halifax home advantage in a one-off play-off semi-final.
"There's huge hunger," Wild said. "Third's the goal.
"Second, there might be a chance now, but two or three is the goal, that's what we need to aim for.
"Look at the graft they put in on Monday to get over the line, after basically waking up Sunday morning, getting on a coach, going down there, five or six hour journey, to put that performance out after what they chucked in when they had to be resolute against Yeovil on Saturday.
"Those boys have put so much effort into last weekend to give themselves a chance to have everything in their own hands going into the final day."
On Town guaranteeing themselves a top four finish in the National League, Wild said: "It's massive, massive. It cannot be underestimated, and it shouldn't be underestimated.
"The players have given everything for this football club, they've left their heart and soul on the pitch, up and down the country.
"With two games to go, to be in this position, I don't think any fan can look any of these players in the eye and say they haven't given everything for this football club."
Wild says the Halifax fans have a part to play on Saturday in what will be Town's final home league game of the season before the play-offs get underway.
"We want to thank them, we want them to come down so we can thank them at the end of the game," Wild said.
"They need to get behind us, they need to drive us forward.
"The atmosphere, certainly in the last 10, 15 minutes on Saturday was fantastic, and we're going to need that.
"Even when you're nervous, just allay the nerves by banging the drum and singing along, even if you don't normally sing, get behind us and sing as much as you can."
Wild said captain Niall Maher, who has missed the last two games with an abductor injury, should have a chance of being fit against Aldershot.
"He just didn't make it on Monday but we're hopeful he'll be in contention for Saturday," said the Town boss, who also said defender Tom Bradbury is on target for being in contention for next Sunday's game at Stockport.
Wild also said midfielder Jamie Thomas was due to report back to training tomorrow (Thursday) after illness.