The Belgian has endured much criticism for his displays this season, with Liverpool struggling to recapture the form they showed when finishing runners-up in the Premier League last term.
Mignolet presented Leicester City's Esteban Cambiasso with an open goal thanks to a careless pass during Tuesday's 3-1 victory, but the Argentinian let the keeper off the hook by shooting wide.
Mignolet was then unfortunate to concede an own goal as a shot from Leonardo Ulloa rebounded off the post, hit him on the back and went in, and Rodgers came to his number one's defence on Thursday.
"Simon Mignolet is working very hard on the training field to improve," he said, speaking ahead of Saturday's clash with Sunderland.
The midweek win at Leicester means Liverpool have put together back-to-back top-flight victories for just the second time this season, and Rodgers was full of praise for the manner in which his players have reacted to a difficult spell that saw them lose four in a row in all competitions.
"It's a really exciting period," he added. "The players have shown the character I always said they had. They have responded magnificently."
Mario Balotelli (groin) missed the game at Leicester and remains sidelined ahead of the weekend as the Football Association continues its investigation into a controversial social media post made by the Italian earlier this week.
However, Rodgers insisted he has not lost faith in the former Milan man, and also hopes to welcome Philippe Coutinho and Jose Enrique back into his squad this weekend.
"He [Balotelli] is injured at moment but he's still very much a Liverpool player. My concentration is on those fit and available," Rodgers noted.
"Coutinho had a slight issue with his knee, but should be OK for Saturday [against Sunderland]. Enrique has trained and should be OK."
One major source of frustration for Rodgers this season has been the continued absence of Daniel Sturridge.
The England striker, who scored 21 Premier League goals last season, has not played for Liverpool since August due to various muscle injuries.
Sturridge's latest setback is expected to keep him out until January, although Rodgers said the 25-year-old is progressing well in his rehabilitation.
"He has gone away to get some work in, with some of our staff, doing specific work," the Northern Irishman continued.
"He's coming along well."
