Portnow said he hoped their dialogue would create better awareness and understanding.
"The place to start is that everybody understands what we do, how we do it, why we do it," he said.
Portnow defended this year's results, which included indie-rockers Arcade Fire's win for best album. He said their victory reflected how the Grammys have evolved over the years.
"Frankly, I'm not so sure 10 years ago where an Arcade Fire could have received a best album (award)," he said.
"This is not about popularity or about sales or even about notoriety, it's about excellence in music," he said. "That's why a Grammy means so much to an artist when they get one, because it's a peer recognition."
But Stoute said the voting Academy, which he said numbered 12,000, needed to be younger and more culturally diverse. He said he hoped that he and the Academy could push to get those demographics involved in the process.
He said some of those segments aren't an active part of the Academy because of years of frustrations.
"There's a segment of artists who have gotten so frustrated with what's going on that they felt like voting and being a part of trying to promote change wasn't going to make a difference," he said.
Stoute also said the Grammys need to reflect the changing way music is made. For example, he said songs with samples aren't permitted to be contenders for song of the year, which leaves out a lot of rap.
He stressed that he wasn't saying the wins of Arcade Fire or Spalding weren't worthy. However, he noted that Spalding had already released two other albums and technically, wasn't a new artist; the Grammys allow for people to be nominated although they have had albums released previously if their latest album represents a breakthrough year and they haven't released more than three.
He also mentioned that Arcade Fire, up for best alternative album, lost in that category yet won overall album of the year.
"They're not even the best in their genre, so how does that work?" he asked.
But Portnow said the Academy routinely looks at its own rules and adapts to the times; for example, this year, the Grammys changed the best new artist criteria so an artist who had been previously nominated for a Grammy but had never won could qualify; it was instituted after Lady Gaga was ineligible for the 2009 award because she was nominated for her first dance song the year prior.
Stoute said, despite the frustrations with the Grammys, they are still the pinnacle of achievement for a musician.
"It's not like people don't respect what the Grammys mean. The Grammy is artistic excellence, you just want to make sure that everybody in the music business gets a chance."