Coutinho, who played only one pre-season game due to his late return after featuring for Brazil at the Copa America, was set to be replaced by Danny Ings as Liverpool searched for a winner.
But with four minutes remaining, Coutinho shrugged off the challenges of two Stoke players before hammering a shot from distance past goalkeeper Jack Butland.
“I was very close to taking him off,” Rodgers told reporters.
“We were looking at making a positive change - so he was going to come off and we were going to put Danny Ings on.
“It was a great strike to win the game.
“I'm glad I kept him on.”
Liverpool finished a disappointing sixth last season and Rodgers received criticism from disgruntled supporters, but the Northern Irishman kept his job following an end-of-season review by the club's American owners.
Rodgers revamped his squad over the close season and new signings Christian Benteke, midfielder James Milner and defenders Nathaniel Clyne and Joe Gomez all started at the Britannia Stadium.
Liverpool face all of last season's top five away before the end of November in a tricky run of fixtures, but Rodgers praised the way his new recruits had handled an always combative Stoke.
“The players that we brought in have that character,” Rodgers said.
“Look at Benteke up front; people talk about him only being a player that can play off a long ball, but you saw his quality today - his setup of the game, his movement, his strength, his power and that ability in the air.
“Young Joe Gomez, at 18 years of age, playing against a really good player in Jonathan Walters, I thought he handled it and as the game wore on he became even stronger.
“Nathaniel Clyne has been outstanding since he came in, James Milner has that experience.”
Liverpool were humiliated 6-1 by Stoke on the final day of last season and Rodgers was delighted to be able to right a few wrongs.
“I knew it was a one-off but it still happened and you have to be better and be more resolute,” he said.
“It was a very good victory for us.” – Reuters
Original source: Coutinho bags points for Reds