Smith ignores Old Firm controversy for three points
However, the aftermath of the first derby of the campaign has been dominated by the debate over referee Willie Collum's performance as he took charge of the famous fixture for the first time.
It has since emerged that Collum has received threats against himself and his family, with the fallout from the match earning far more exposure than the performance of the winning team.
Smith said: "All the circumstances that surround Old Firm games, including the effects of a win or a defeat or a referee's performance or a manager's performance, are all exaggerated to a great degree.
"We are just happy that we managed to win at a place that has been an extremely difficult place for us to get a win.
"We are just happy about that and the rest of the stuff that goes on around it is stuff we cannot do a great deal about.
"It was an important game for both clubs and we were fortunate enough to win it but we are hardly a quarter of the way though the season and there is a whole lot of football to be played."
"We don't have a large group of players and we are going into a League Cup tie with Kilmarnock with one or two of our players looking as though there is a bit of tiredness there," Smith admitted.
"We have had some big games as a club and we have also had some big games internationally with a number of players involved in that arena as well.
"There is a lot of football to be played and we only have a small group of players so we are already seeing that we are putting them under a little bit of pressure.
"We have to make sure we are right and it makes Wednesday's game an awkward game for everyone.
"The size of our squad may determine ultimately, depending on injury and suspension, how we get on.
"We have shown we can acquit ourselves well with the group we have, but the aspects which are difficult for us to handle would be the injuries and suspensions.
"That can upset our season, we know that, and we are just pleased we have started the season the way we have.
"We are asking a lot of a small group of players to handle the situation."
Despite concerns over the size of his squad, Smith does not expect to be given cash to strengthen in January.
"I don't think so," he said. "It doesn't look like it at the moment."