Red Bull announced on Friday that it had signed outgoing Racing Point driver Sergio Perez for next season to replace Albon, who has dropped into a reserve and test role.
Red Bull has been considering Albon's future for some time after he struggled to match teammate Verstappen through 2020, but wanted to give him until the end of the season to stake a claim for the seat.
But after Perez scored a victory for Racing Point at Sakhir and Albon returned just two podium finishes all season long, it took the decision to draft in the Mexican driver.
While Horner felt Albon had "improved significantly", he said the gap to Verstappen had remained the same throughout the year.
"You take what you've got, don't you?" Horner told select media including Motorsport.com when asked if Albon had been unlucky with the RB16 car.
"He's in Formula 1 and graduated to F1 because of Red Bull which he's very grateful for. He's still part of the team.
"This year's car has been tricky. I think it's improved significantly throughout the year, particularly in the last third of the year. But, again, it's what you make of it, isn't it? I think the gap between Alex and Max has largely remained consistent from Austria to certainly Bahrain 2. He had a good race in Abu Dhabi.
"Everything else, he's done brilliantly well. He's a great racer, he's an absolute gentleman within the team. He's very popular within a team because he's such a nice guy. That's what's made this decision harder.
"But when you look at the data and you trust the facts opposed to emotion, Sergio is the logical choice."
Horner said that Albon was informed of the decision on Friday, and was "obviously disappointed" but "incredibly mature" in accepting the news.
"He's grateful for the opportunity and support that he's had this year, and obviously determined to do the best he can to get back into a race seat for 2022," Horner said.
Asked how Albon could make a case for a race seat in his test and reserve role, Horner said Red Bull would "see how things unfold".
"He's got an important role in terms of development with 2022 and tyre testing, and obviously the development of the 2022 car in the virtual world," Horner said.
"We'll see how circumstances how circumstances unfold for 2022, either within Red Bull or external to Red Bull."
Red Bull has struggled to field two competitive cars since Daniel Ricciardo's exit from the team at the end of 2018, with Albon's predecessor, Pierre Gasly, experiencing similar struggles during his 12-race stint at the team last year.
Horner said it was crucial for Red Bull to give Verstappen a competitive teammate to help in the fight against Mercedes after being left without a rear gunner at races this year.
"I think it's vital if you want to mount a serious challenge in either of the championships, that you need both cars performing at a level," Horner said.
"We saw that very clearly in Abu Dhabi, for example. So you need that consistency, in order to take on the likes of Mercedes in either the drivers' or teams' championship."