The visitors held off a spirited second-half display from Paul Lambert???s side to move within four points of the Premier League???s top four.
Mignolet produced an excellent stop to deny Christian Benteke with the score at 1-0, and Rodgers was full of praise for the under-fire goalkeeper, who has now kept five clean sheets in his last seven Premier League games.
???In the second half they made a good start as you???d expect from a home side, but we were resilient and strong today, and defended really well,??? he said.
???I thought the goalkeeper ??? what he had to do ??? was outstanding. Simon Mignolet really grew for me today as a goalkeeper.
???He was very dominant against some players who are really good in the air, came and took his crosses well, and made two very important saves for us when he was called upon.???
Fabio Borini was given the nod up front by Rodgers, and rewarded his manager???s faith as he put the visitors in front halfway through the first half.
The Italian had been linked with a move away from Anfield but Rodgers was delighted with the striker???s professionalism.
???He???s very strong minded, Fabio,??? he said. ???He hasn???t been in the team and hasn???t featured a great deal, but what he hasn???t stopped doing is working.
???His perseverance is a great example, but I think he knows I???m the type of manager where it???s never personal with a player, whether he stays or goes.
???If he???s contributing, working hard, and shows that he cares then I???ll always give him the opportunity. He???s done very well.???
Raheem Sterling returned to the Reds??? line-up at Villa Park after being given a rest for tiredness, and Rodgers said the break was not just for him to help Liverpool???s top-four push this season, but also to benefit the England international???s long-term career prospects.
???Giving Raheem a break wasn???t just a short-term thing ??? it???s for his career. He???s just turned 20 years of age, he???s played more minutes for us than anyone.
???He???s a real catalyst for the team and we???ve got a very important second part of the season. I thought he did very well today ??? should have scored and he???ll be disappointed with that, but as always with Raheem he???s tireless and a real threat.???