Albon scored top-six finishes at every race for Red Bull except Brazil, when he made contact with Lewis Hamilton on the penultimate lap of the race amid a battle for second place.
Horner hailed the Thai-British driver's ability to learn quickly and understand F1, having been thrown into the deep end early on in his career.
"It’s easy to forget that it is his first year in Formula 1," Horner said. "He’s getting better and better understanding the tyres, the complexity of how the cars operate. You see on Sunday that his pace is getting closer and closer."
In Abu Dhabi, he was quicker than Sebastian, to be honest with you. We tried to get ahead of Sebastian with his slow pit stop, but didn’t quite make it.
"Then after he was able to run easily at his pace. His pace is definitely is getting stronger. A proper winter, pre-season, he knows the drill in F1. He’ll go to Melbourne a much better-prepared driver."
Red Bull ended the 2019 season with a strong car compared to where it was in the pecking order at the start of the season.
It has been a common theme of the energy drink squad over the last handful of years, however with little changes in the regulations coming for 2020, Horner is hopeful that the team will start the year strongly
"Going into next year, we have stability of regulations, so theoretically, the car that you see in three months will be an upgrade on the car that is here.
"It would be very unusual to get any team to completely abandon a concept and it feels like we’re on the right trajectory. Unless we miss something, hopefully we can be competitive from the start of next season."
Bahrain International Circuit - Winter testing