Despite the 1-0 scoreline Rangers were comfortable winners away to form team Hamilton.
Gers captain Barry Ferguson decided the spoils with his first goal of the season in the first half of a game dominated by the visitors.
"Barry's first goal of the season was a good one for us to get," he said.
"Maurice Edu came in and I thought Barry and Maurice played extremely well in the midfield.
"Hamilton crowd that area of the field and make it difficult for teams in there but I thought both were excellent."
Smiths says Edu has to be patient but assured him his time will come, adding: "I did say to him, as has happened with a number of the lads who come to play for the Old Firm, it takes a period of time to settle in.
"Him especially, because he was playing college football in America up until a year and a half ago and then one season in the MLS.
"He is still young in terms of his experience at professional level and it will take him a bit of time to come in. But I think he has the talent to be an exceptional midfield player."
Smith continued: "It was always going to be a difficult challenge for us and I was delighted with the way the team went about the game.
"Hamilton have made it a very difficult place to come and get a result and that's credit to them.
"I was a little disappointed that we weren't tidier in our final pass, especially in the final half hour of the game where we might have given ourselves a level of comfort.
"We allowed chances to go past and it's always a bit nervy towards the end of the game. But I thought we were excellent overall in terms of our defending."
Hamilton boss Billy Reid had no complaints about the result and any reservations he had about the officials he kept to himself.
"I don't think I can comment on the referee," said Reid.
"But the one thing I will say is that we were disappointed not to get a foul just before the goal. I thought Kris Boyd lunged with two feet and it was a foul."
As to the game itself, "We never created enough and we had no cutting edge.