Goals from Liam Miller, John Rankin and Francis Dickoh sealed the shock win for Hibs and inflicted a first Clydesdale Bank Premier League defeat of the season on the Scottish champions.
Asked if fatigue was a factor, Smith said: "You can always use tiredness but it's not an excuse. You have to give credit to Hibs for the manner in which they played. That's the main aspect.
"Over the last four or five games, I've maybe asked too much of too many, I should maybe have changed the team around a little bit.
"We didn't have the required sharpness to break down a Hibs team who were playing exceptionally well.
"At the end of the day, we've got no complaints. Hibs played very well and worked very hard on the evening and deserved their win."
He said: "That's not got much to do with it. I've said before that teams will drop points.
"After the first quarter of the season we have lost one game and drawn one and that's a fairly normal situation to be in. We obviously don't want it and we certainly didn't want to lose tonight's game.
"We've had warnings, in the previous home match against Inverness we were very similar in that we had a lot of possession of the ball but the required edge was missing.
"That's something we have to adjust and, from my side of things, I've maybe been a little bit slow to change the team around."
The win was Colin Calderwood's first as Hibs boss and he wants more of the same against Motherwell at Easter Road at the weekend.
He said: "This was a terrific win. I wanted the win to be before now but it is a stand-out victory whenever you come to any of the Old Firm grounds and get anything, it's quite an occasion. It's one that I will remember for a long, long time.
"It's a momentous victory and there will be a few raised eyebrows all over the country, especially in England I would imagine.
"It's all about the weekend and what I really want is a performance that will have the fans on their feet, like they were at the end of this game. I want people to come back to Easter Road and enjoy a resurgent Hibernian team.
"This is a snapshot and we've got to make sure we turn it into a picture album."