But 10-man Hearts stunned their hosts when Scott Robinson netted just two minutes after the dismissal of Christian Nade, with only a last-minute strike from youngster Andrew Little rescuing a point for Rangers.
Smith said: "Before the game, you are always thinking you are at home and that you're going to win the games.
"We don't drop that many points at home so, before the game, we would have been looking at it like that.
"But, in the context of the game and the way it went today, we are happy to get a point in the end."
Smith had four youngsters - including Little - on the bench and 18-year-olds John Fleck and Danny Wilson in the starting line-up.
With Kris Boyd, Kenny Miller, Nacho Novo and Steven Naismith all injured, Kyle Lafferty was the only first-team striker available on a day when Rangers struggled to find the back of the net.
But Smith said: "Injuries happen to all the teams throughout the season and you have to cope with that.
"The difficulty that you have - and that we are having at the moment - is that you have to pitch people in who haven't been playing on a regular basis.
"They are not always up to full-match sharpness and that's one of the difficulties of having to do that.
"Against a team like Hearts, whose basis is a strong one, we would need everyone as sharp as they can be and when we did have a couple of opportunities today we missed out."
According to Smith though, the one bonus of having so many regulars unavailable is the next generation being given the opportunity to impress in the first team.
He added: "I felt John Fleck played well today. It was his natural position he played today and he was a little unfortunate not to get on the scoresheet with a couple of good attempts.
"It is an awkward situation for the young boys to come in and handle for the simple reason that they haven't played an awful lot of games during the season.
"The benefit that the likes of John Fleck and Danny Wilson are getting just now is that they're showing everyone they can play. That's a big step forward for them at their age considering they are just 18."
Rangers face St Mirren midweek and the manager does not expect the injury situation to improve dramatically before then.
He said: "Beasley and Naismith are close to coming back but we will have the same problem we had with Pedro Mendes.
"Mendes was not fit to play today but we had to put him on the bench because of the lack of numbers.
"It will be the same with Beasley and Naismith when they do come back, it's the awkward situation of trying to fit them into the team at the right time and hope they can get up to speed right away.
"But we would be pleased to have them back and they should be there or thereabouts for Wednesday or the weekend."
Meanwhile, Smith was unsure whether Jerome Rothen - who has been back in France with swine flu for several weeks - had sealed a loan move to Turkish side Ankaragucu, as reported earlier in the day.
He said: "Martin [Bain, chief executive] was dealing with that one. I think he is going there, although I don't think it's confirmed yet. But I think he is hoping to go there."
Reflecting on the game, Hearts manager Csaba Laszlo said: "Maybe if we had a bit more experience, we wouldn't have lost the goal because Rangers only had one chance in the game.
"Even that chance was created by our own stupidity. But, overall, I must compliment my team for their performance in this game.
"We could have done some things better but I think we can hold our heads up high in George Street in Edinburgh tonight."
Laszlo felt Nade's first booking was harsh but was furious the player picked up a second caution just four minute later for kicking the ball away in frustration.
He said: "I'm very angry that a player in his situation would do this. It was a second yellow card, definitely. But he already had a yellow.
"My opinion was that the goalkeeper and defender collided and Christian wasn't involved in that case but he got the yellow card and you must accept that you can't do what he did afterwards.
"But, for me, the biggest punishment is not having him in the squad now. Fining him won't resolve anything."
Source: Team Talk
Source: Team Talk