Carter, who has amassed a record 1250 points during his 85-cap Test career, tore a groin tendon in kicking practice last Saturday, ending his participation in the tournament and leaving a nation wondering whether their 24-year wait to lift the William Webb Ellis trophy can be realised without the inspirational playmaker.
Slade assumed the number-10 jersey for Sunday's defeat of Canada and has been backed by Carter, head coach Graham Henry and now his assistant Smith to help the All Blacks to World Cup glory.
Smith said: "Plans remain the same - expectations are exactly the same, belief of the squad is exactly the same. We don't see anything's changed.
"If you walk in the company of people who believe in you, you can achieve anything.
"He (Slade) has got a good skillset. He's a brave kid physically, he's strong in his defensive channel. So not too different to Daniel really.
"He's got all the tools to make a go of it and he's got the belief and encouragement from the squad."
New Zealand eased to four wins from four matches in Pool A and face Argentina in Auckland on Sunday, with a semi-final place at stake.
Smith added: "They're going to be a physical test, they're going to be a tactical test, because they're very smart.
"They're tough physically. They take a lot of pride from their pack. They've got a very good defensive system.
"They don't over-commit there, they've always got players on their feet available."
While Carter and captain Richie McCaw, who is set to return from a foot injury against the Pumas, missed the win over Canada, number eight Kieran Read returned.
Read, who was pleased to come through the match without any adverse reaction to his ankle problem, admitted the squad are suffering without Carter.
But he insisted the 30-man squad - with Aaron Cruden replacing Carter - must deliver as a unit for World Cup success.
Read said: "We're hurt, man. He's a massive part of this group so within the squad we definitely are hurting for him.
"It's really tough but what we've got to do is move on from that. It's a tough challenge and the strength of our squad is what's going to win us this World Cup.
"Colin is a pretty cool customer, he's got a level head on his shoulders.
"We're a team of 15 of 30 guys so we expect that whoever is going to play will do the job and do it really well."
Read is wary of Argentina, but believes the All Blacks can raise their game further.
He added: "The Pumas are a dangerous side. Their strength is in their forwards, and I think there's no hiding behind that.
"They're really going to attack us in that area and they'll really look to try and work territory and kick really well and try to keep the scoreboard just ticking over against us.
"We've been improving in a lot of areas but we know we can go up another notch in quite a few different things.
"A quarter-final, a one-off game, is the test for this group, so that's our major focal point."
Gilbert has released a new line of rugby cleats. The Gilbert Virtuo 8S is part of the exciting new product. Check it out.
The entire All Blacks apparel line has been updated for 2013/14. Check out the New Zealand All Blacks polo.
The Nike Tiempo is a solid rugby cleat and one of few styles still made from full-grain natural leather.
The Gilbert Blitz 8S rugby cleat is a great cleat at a great price of $69.99. Get a new pair of cleats today.
A cool looking all black rugby cleat with the high performance adidas is known for. Get in the Gear!
Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
The All Blacks Performance t-shirt is black with hints of blue from the training jersey. Very Cool.
The New Zealand All Blacks training jersey for 2013/14. Get in the Gear!
The USA Rugby Pro Alternate rugby jersey is perfect for any fan of the Eagles. Get yours to wear during the summer Test matches.
The NEW All Blacks 2013/14 jersey has arrived at World Rugby Shop. Dare to wear the colors of the All Blacks.