Virtue scored twice while Brewster got on the scoresheet and provided an assist in the victory at Prenton Park. Dhanda also made an impression with a superb cross that led to the opening goal.
Critchley fielded a strong side, with Melwood-based players Danny Ings, Marko Grujic, Ben Woodburn, Ovie Ejaria and Ryan Kent all given minutes.
Reflecting on the win over the young Black Cats, Critchley told Liverpoolfc.com: "I thought we made hard work of it for long periods, particularly in the first half.
"We were too slow and didn't play forward enough, but in the second half we were much better and more on the front foot.
"The substitutes we brought on made a huge impact and made a big difference to the team, bringing energy and life, so in the end I'm pleased with lots of positives to take, but for long periods we could have done more as well."
LFCTV GO: Watch highlights of the 3-0 win
The coach also reserved special words for Virtue, who netted a double and was influential in the victory.
He added: "I thought Matty was outstanding when he came on and made a huge difference to the team.
"He was a victim of circumstances a little bit with the team selection, but he is so level-headed and humble and he doesn't let it affect him.
"You could see that when he came on. He got into the box and made some really good runs and got his reward for it. I was absolutely delighted for him."
Brewster endured a disrupted start to the campaign when a broken bone in his foot kept him out of action for most of the pre-season programme.
But the 17-year-old showed he is getting back to full match sharpness during Sunday's outing as he claimed his first goal of the season.
"It was a lovely touch and run from Rhian and he finished it off well after a lovely pass from Ovie [Ejaria]," Critchley added.
"It was also nice to see Rhian have a hand in our third goal and he was really lively when he came on.
"We have got to try and give Rhian more minutes and build up his fitness because I think he can be even better when gets into a rhythm of playing games.
"It was good to have some of the Melwood-based players with us because they needed a game. Danny [Ings] always offers something up front and he could have had what would have been a fantastic goal towards the end of the first half."