Mercedes is upbeat about its prospects for the rest of the season after a major upgrade package to its W14 helped Lewis Hamilton and George Russell produce a double podium finish in the recent Spanish Grand Prix.
It came after a difficult start to the campaign where the German manufacturer quickly realised that its 'zeropod' concept was not going to deliver the performance it needed to take on Red Bull so it has to change its design.
But despite the impressive step forward Mercedes made at Barcelona, Horner has said that his rival's form needs to be put in context.
He suggests that the extent of changes Mercedes made will have eaten into a lot of its development budget, which means there may not be much money left over to make further upgrades over the remainder of the campaign.
Furthermore, he says that Hamilton finishing 24 seconds behind Max Verstappen in Spain was similar to Fernando Alonso coming home 26 seconds adrift of runner-up Sergio Perez in Bahrain, so suggests the gap to the opposition is not getting much closer.
Asked by Motorsport.com how much genuine progress he felt Mercedes had made, Horner said: "For sure they've made a step.
"But they've introduced pretty much a B-spec car, so they must have used a significant proportion of their development budget on that.
"And I think that when I look at the gap at the end of the race, it is very similar to where it was in Bahrain.
"All that is happening is the running order behind us seems to vary from race to race. You know, Fernando last weekend [in Monaco], Mercedes this weekend. It will be interesting to see how that plays out over the next few races."
Horner says that his team deserves praise for the way that it has been able to maintain its advantage in F1 despite having only made small improvements to its RB19 challenger.
"The team are just doing an incredible, incredible job being extremely efficient," said Horner. "You can see we've very subtly developed the car since Bahrain, while we've seen others bringing significant upgrades now.
"The margin has remained pretty much the same from where it was in Bahrain, so that's hugely encouraging to everybody in Milton Keynes that is doing an outstanding job at the moment."
