Last time out in Hungary, Albon crossed the line on Sunday in fifth place following a disappointing qualifying session that saw him drop out in Q2.
It marked his second top-five finish in two races, however his weekend at the Styrian Grand Prix was also called into question as he was unable to keep up with teammate Max Verstappen and the Mercedes duo.
Horner says that Red Bull must take some responsibility for his poor qualifying result in Hungary, but insists the team is pleased with how the Thai-British driver recovered his weekend.
“He's driven a great race. From where he's come from on the grid, racing Ferraris, the party moves he made, all credit to him. He made a great recovery,” Horner told Sky F1.
“He's picked up a bit of criticism which is being very, very harsh on him. On Saturday we made a mistake on the timing, we put too much pressure on him. We have to take responsibility for that.
“We apologised to him. He's done a great job. He's done the passing manoeuvres he's needed to, he's responded very well. I really believe that Alex has got a lot more potential that we just haven't uncovered yet.”
Heading into the 2020 season, Red Bull was being tipped to challenge Mercedes for the world championship, however after just three races, the energy drink-backed squad is 66 points down on the German manufacturer.
Horner says the RB16 is currently “very difficult” to drive, with Verstappen's experience assisting him on the timesheet compared to Albon, who is currently enduring his second F1 season.
“The car is very difficult at the moment and Max's ability to drive around those problems... his DRS wasn't even working into the Turn 1 in qualifying if you look at his lap,” Horner said.
“He's totally sideways and he's still able to catch it. That's experience on Max's side that Alex doesn't have. The only way to get that is to go to the events, go through the emotions. He will get, and is getting, stronger and stronger.”
Bahrain International Circuit - Winter testing