The Thai-British driver produced a strong fightback which included some breathtaking moves at turn one to help secure his long-awaited top-three finish.
"I'm really pleased for him because he has weathered a bit of criticism," said Horner via Sky Sports F1.
"To be fair, the last couple of weekends, he has been getting stronger and stronger and for him to get that podium, he had to really fight for it, he had to do it the hard way. The starts were pretty horrible, but he is 'Mr Around-the-outside'."
To move into the podium positions, Albon needed to find a way past former Red Bull driver Daniel Ricciardo.
The Australian is recognised as one of the hardest racers on the grid, but Albon produced a move straight out of Ricciardo's play book to secure the silverware.
"He is really impressive," added Horner. "We see it time and again with him that his placement of the car is very, very good.
"Daniel is a hard guy to pass and to make that move around the outside and make it stick, all credit to him."
Crediting Albon with maturing development since joining Red Bull last summer, Horner said: "His feedback is very, very good.
"He has a really good sensitivity with the car and I think he has won the respect of the engineers with that so as that is now starting to come through, the developments are starting to come. It will only help him."
GPFans is a multi-platform, multi-language brand dedicated to Formula One coverage. We bring you all the ins and outs of the sport, 24/7, everything from up-to-the-minute news and features to the latest viral stories and clips.
We believe that a new generation of exciting, outspoken drivers will make F1 more popular than ever before, and we want to give our users access to as much of their heroes as possible, on and off the track. From Lewis Hamilton to Max Verstappen, Daniel Ricciardo to Sebastian Vettel, we provide in-depth analysis of every every Grand Prix in the season, from Australia to Abu Dhabi.
With Formula One under the new ownership of Liberty Media, how the sport is being covered is evolving, and GPFans will look to be at the heart of this progression into new media, as one of the fastest-growing sites covering the king of motorsports.