But he looked largely comfortable throughout the day as Brawn appeared to exhibit their continuing strength.
"I am delighted to welcome Paddy to the team and to begin working together, " said Brawn.
Brawn oversaw all seven of Michael Schumacher's world titles in addition to Jenson Button's in 2009.
The result also means that Button's Brawn GP team have claimed the constructors' title.
Brawn returns to work with Ferrari on 5 January for a week's testing in Jerez.
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"There's nothing about this car that makes me think it'll have any bad tracks, " Brawn says.
Brawn said he was not yet able to say how his two drivers compared on performance.
BBC: Ross Brawn says top Formula 1 teams are closely matched
The new machine age is more about knowledge creation: brains not brawn, ideas not things.
Ferrari technical director Ross Brawn agreed that Schumacher was enjoying his racing as much as ever.
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Button's team-mate Rubens Barrichello endured an incident-packed race but was impressed with the Brawn's durability.
Brawn have been taken over by Mercedes and will race as Mercedes Grand Prix next year.
Which is better: brains and brawn, or giant claws and a mouth full of teeth?
Brawn's Rubens Barrichello, fighting with Vettel for second in the championship, will start fourth.
Brawn refused to criticise Barrichello for Sunday's outburst and said he sympathised with his driver's frustration.
One reason is that conservative brawn has lost patience with brains of all kinds, conservative or liberal.
Did you get these things done through sheer force of will, with your bare hands and brawn?
The car on show was one of last year's Brawn cars in the new 2010 colour scheme.
Brawn said he was confident the team would be able to build on this year in 2010.
The party's electoral success from 1980 onwards was driven by its ability to link brains with brawn.
Team principal Ross Brawn is going back to their Brackley HQ with a shopping list of updates.
Brawn said he would listen to Barrichello's interview again before deciding whether to take the matter further.
Mercedes announced on Tuesday that they were selling back their 40% shareholding in McLaren and buying the Brawn team instead.
The German's team-mate Nico Rosberg finished fifth to cap off a good weekend for Ross Brawn's team.
If exporting brawn generally makes sense for a poor country, sending its better brains away may not.
Barrichello and new world champion Jenson Button dominated the early part of this year's title race with Brawn.
That released Vettel, who had a 10.5-second lead over Button when the Brawn emerged from its pit stop.
Now Mercedes are understood to want him to launch their return to F1 following the takeover of Brawn.
Ferrari were quick enough in Monaco that Brawn's race day victory effectively hung on Button's near-perfect qualifying lap.
That positioning was a result of the very small but decisive pace advantage of Button's Brawn in qualifying.
Unless there is a wet race in Hungary, I don't see how Brawn can fight back from there.
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