McLaren announced on Wednesday that it had come to an agreement for Ricciardo to leave at the end of this season, a year before the scheduled end of his contract.
While acknowledging that performance on track was the deciding factor in the decision to part company with the 33-year-old, Brown made it clear that Ricciardo had been a "positive influence" in several ways.
"I think there's a lot we're going to miss about Daniel," he said. "I think he's brought a lot to the table.
"Let's start with Lando. Ultimately you want a data point against your teammate. We know how capable Daniel is, so to have Lando running as competitively as he is, I think Daniel has helped Lando step up.
"I think commercially and with fans Daniel has brought a lot of energy to McLaren and our racing team. When you have a seven-time Grand Prix winner joining your team, it certainly brings a lot of enthusiasm to the racetrack and the factory floor.
"His work ethic is fantastic. And his positive outlook – when you have a bad day he's very quick to bring positive energy into the environment.
"And then of course, our win in Monza was awesome, and being on the podium and celebrating in a tattoo parlour in the US is going to be something that we never forget.
"And so I think there was a tremendous amount of positive influence that Daniel had on our team."
Asked if ousting Ricciardo was the saddest decision he's ever had to make Brown admitted that it had a personal element to it.
"Yeah, certainly, during my time at McLaren," he said. "Daniel is a wonderful person, and a great person to be around. We've had many laughs, we've sprayed champagne together.
"And yeah, it's very personal. So today is a sad day, that things didn't work out as we'd hoped they would. I'm going to look back with some very fond memories, some fun times together, on and off the track.
"We're in a business. We need to focus on ultimate performance, and wish Daniel the best. There's absolutely no ill will between us, it's all very amicable.
"And I think he too has had a very good time at McLaren. And he's young, so we hope to see him in a competitive racing car. And one of these days we might see him being a pain for us on the race track, and that'll be fun, because he's a great competitor."
McLaren team principal Andreas Seidl also paid tribute to Ricciardo on a personal level.
"I'm obviously disappointed that we didn't manage to make it work," said the German.
"But the respect I'm having for the person of Daniel Ricciardo, but also the race driver, hasn't changed. I'm still convinced that he is one of the best ones that is around in this paddock.
"And in the end, we think joining the team one and half years ago, with everything he brought to the team, with his experience also, it definitely helped us a lot to become, in the end, a better team.
"And I really always appreciated a lot his positivity, his enthusiasm, and help also, helping me in difficult situations like the start of the season, where we had some tough times going to the first race.
"He never gave up, and always helped me, also keeping the team in a good shape, and he helped me to keep to pushing forward and say stay motivated and stay flat out in order to not give up. And that's something I would definitely miss from him."
