Barry struck early in the second half of Monday night's 1-0 victory at St James' Park, securing Everton's first away win in the Premier League this season. It was his second goal against Newcastle in four days and his eighth in 12 appearances across all competitions.
Only Manchester City's Erling Haaland, with 13 goals, has scored more among Premier League players in all competitions this season.
Dewsbury-Hall believes the forward's willingness to keep getting into dangerous positions will continue to bring rewards, even when his goals are not spectacular.
"I just said to him in the dressing room after the game that he will score five or six of them a season, from a yard out no one will remember the goal but they will just see his name on the scoresheet to win the game.
"He will keep getting the right position again and again, and the law of averages say you will score a goal, so I am buzzing he has done that tonight and I just said keep doing what you are doing because it is really good for the team."
The midfielder has also been impressed by the work Barry put in during the summer after finding his first season in English football difficult.
"He needs to rest and recover because he is playing a lot of minutes, but I am really liking his attitude this season.
"He's shown a fantastic attitude coming into this year. It is really tough to come into the Premier League in your first season from abroad.
"And he probably saw that and had to deal with that. And it was probably a shock for him, but he's gone away in the summer and he's worked tremendously hard.
"He has come back with a point to prove and a bit between his teeth and I’m very, very, impressed with his attitude for a young lad and he’s only going to go from strength to strength."
The victory lifted Everton to seventh in the table, with Dewsbury-Hall pleased by the collective effort after another demanding match against Newcastle.
"A hard-fought win, but a really good performance, I thought," he said. "All aspects of the game: attacking, good quality for the goal, but defended well for the team.
"Everybody put a really good shift in, especially after the game four days ago, I am really pleased with that performance, a good away win and a clean sheet."
Dewsbury-Hall is also hoping his club form will earn him a first senior England call-up when Thomas Tuchel names his squad on Friday. He was previously placed on standby for the Nations League fixtures and remains determined to force his way into the plans.
"I said it publicly that is what I want. I know the better I play for my club the better chance I have of featuring for my country. I will keep plodding along and see what happens."