The team were reprimanded and ordered to miss a three-day young driver test in July after an independent tribunal hearing decided they had broken the rules by taking part in a tyre test with Pirelli in Spain in May.
Other teams protested when they found out about the test but the tribunal ruled Mercedes had acted in good faith and not sought an unfair advantage.
"I think these events are the ones that pull the team together. These are the sort of events as well as racing that consolidate a team," Brawn told Sky Sports television after the verdict.
"I think the team was very solid in the last few weeks, we had complete support from (Mercedes headquarters in) Stuttgart. They understood...it was very important for Mercedes that the facts of this case were understood."
Asked whether he had feared a different outcome might have hastened his exit from the team, the Briton acknowledged he had been under some pressure before the hearing in Paris.
"An event like this creates a lot of emotions. It would have been very frustrating if the outcome of this hadn't been what it was...but it does sometimes strengthen your resolve rather than weaken it," he said.
"It's certainly cleared everything away now so we can focus on the rest of the year. The car is coming along well, we've got some interesting things to try at Silverstone, some improvements, and two drivers on top of their form.
"So I think we can now move on to the rest of the season. Certainly it hasn't diminished my enthusiasm for Formula One."
The British grand prix at Silverstone, a short drive from their Brackley factory, is next week with 2008 world champion Lewis Hamilton and Germany's Nico Rosberg hungry for success.
Brawn said the drivers had been kept fully abreast of developments and had been concerned at what could have happened to the team.
"I think they are pleased we've got a balanced result, a balanced conclusion. They are just keen to go racing again," said the Briton.
Mercedes, winners of the Monaco Grand Prix, are currently third in the constructors' championship after seven of 19 races.
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