Defending champion Max Verstappen retired on the first lap after being driven into by Mercedes rookie Kimi Antonelli, while teammate Yuki Tsunoda finished last.
As a result of Lando Norris leading home team mate Oscar Piastri in a McLaren one-two, Verstappen was left languishing 61 points behind championship leader Piastri.
"The buffer they have is significant. It looks very much like a two-horse race. They (McLaren) have got a cushion to the rest of the field," said Horner.
"For us, we focus one race at a time. We don’t even think about championships. We just focus on the next race at Silverstone, what can we achieve there; same with Spa, same with Budapest.
"You try to grab every opportunity like we did in Imola (where Verstappen won)."
Verstappen had qualified a lowly seventh, partly undone by yellow flags as a result of a spin by Pierre Gasly in the final moments of Saturday’s session.
In the race, he was the unfortunate recipient as Antonelli hit him after misjudging under braking into turn three, ending Verstappen’s race in the process.
Tsunoda struggled all afternoon and was later given a 10-second penalty for a clash with Alpine's Franco Colapinto, which resulted in the Japanese driver finishing last.
Ferrari's Charles Leclerc and Lewis Hamilton took third and fourth places to move their team into second place in the constructors' standings.
Horner said: "Well, that was a home race to forget. We got unlucky yesterday with the yellow flag which puts us in a position where you’re unfortunately in the crash zone and Kimi just lost it in spectacular fashion.
"Max was basically through the corner and getting back on the power and he just got wiped out. So, an unfortunate mistake by Kimi. He’s apologised to Max but for us it killed our afternoon.
"I don’t think we should have had the pace to race the McLarens today so well done to Lando. I think we would have been in that fight with the Ferraris. But when you’re out on turn three there’s not much you can do about it."
