Igor Semshov, Sergei Ignashevich and Roman Pavlyuchenko scored the goals for the Russians.
Hiddink said: “We dominated tactically in the first half, and with more accuracy we could have scored more.
“Wales had great spirit, but they did not really create too many chances.
“But we know it is always difficult here in Cardiff, and in the second half we were not at our best and lost some of our positioning.
“We were certainly not determined enough to clear the corner that they scored from.
“But the team responded in the right way to that setback. They did not panic even though they knew that 1-1 was not good enough, we had to win to stay in the race with Germany.”
Hiddink added: “This team has grown, it is more mature and it has learned to play under pressure.
“We knew Germany were winning, and we have now got the right result to go into our showdown with Germany for top spot in October with great confidence.
“I was pleased with Pavlyuchenko when he came on as substitute. He hit the bar and scored a fine goal, that is the player we like to see, in that sort of form.”