It was another difficult weekend for Perez, who only finished fourth in Barcelona.
Perez was knocked out in Q2, while Red Bull teammate Max Verstappen dominated the race from pole position.
Rosberg - who was working as a pundit for Sky Sports in the UK - put the following question to Horner about Perez’s performance.
"You were just saying he did a good race but I thought it was quite a lack of performance, especially during the early part of the race," Rosberg questioned.
"Isn't that true? I mean, comparing to Max there were some laps where there was quite a gap."
In response, Horner pointed out that Rosberg is a “criticial kind of guy” since retiring from F1 at the end of 2016.
“You're a critical kind of guy, aren't you? You're tough on these guys. Now you're out of the car you have to criticise all the guys.
“I think that he [Perez] lost out in the early laps and didn't have a great start. George managed to get away with running off the track and not getting any penalty for that and I think that was the difference at the end of the day.
“Checo's race was getting stronger and stronger and that last stint in particular, he was really coming back very strong, but just not enough laps to fight for the podium.”
Perez now sits 53 points behind Verstappen after seven races.
Horner believes the widening gap in the championship should alleviate the pressure for Perez.
“I think if you look at the points now, there’s a big split between the two of them,” Horner explained.
“If anything, that should take the pressure off him. He has nothing to lose now and he just needs to relax, he can breathe out and just drive like we know he’s capable of, like he did in Azerbaijan and some of the early races this year.
“I think today was a good recovery from him and it will give him confidence as we head to Montreal.”