Kelly suffered the first loss of his career at the weekend and Benn has questioned why his British rival keeps wilting during fights after his sixth-round stoppage.
Benn told Sky Sports: "Kelly was looking sharp, he was accurate.
"He landed some great power shots early on. I thought Avanesyan might be in trouble, but Avanesyan got to him.
"Kelly has got all the skill. He is naturally gifted. Why does he keep blowing up after four or five rounds?
"Maybe it is a weight issue, maybe he should move up a weight, because I like Kelly, I do. I'm gutted for him, to be honest, I really am."
Benn continued: "Everybody knows Kelly is good for four, five, six, but when it gets past that and it gets on top of him, he folds.
"That's what happened tonight. Avanesyan kept applying the pressure.
"He will come back. He's just got to sit down and question how much he wants it."
Promoter Eddie Hearn suggested that the welterweight can still reach the highest level and believes that Kelly came up against an excellent fighter in Avanesyan.
He explained: "Sometimes you come across a guy that will not be denied, that's too strong.
"That has the will beyond others, and tonight that was David Avanesyan.
"Josh Kelly had a wonderful camp. Josh Kelly was in the shape of his life. Josh Kelly couldn't have been better in that ring tonight, but this man, he wouldn't be denied. He was too tough.
"What we saw tonight was an elite welterweight. A world-class welterweight against a really good prospect who I believe can be a world-class fighter. But he was just out-manned, he was just out-hustled, he was just outfought."