Belgian goalkeeper Mignolet said the result was a welcome boost for the fourth-placed club heading into the final stretch of the season.
"We knew beforehand what everyone was saying about how we didn't manage to get results against the 'lower' teams who play a different style of football compared to the top teams," he said.
"Although we went behind, we fought back by playing old school, English football. We fought for everything.
"You have to accept that sometimes you need to grind out three points."
Liverpool have picked up 19 points in nine games against top-six opponents this season and Mignolet said playing better quality sides had suited Juergen Klopp's squad this season.
"Now the next two games are very big - Manchester City and then the derby [against Everton] after the international break," Mignolet added.
"They will be different games compared to Burnley. It's a different kind of game when it's on the floor."
The Merseyside club have an opportunity to move above City into third place with a win this weekend.
(Reporting by Hardik Vyas in Bengaluru, editing by Nick Mulvenney)
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