The Clarets took the lead over Jurgen Klopp's side through Scott Arfield and, while they were quickly pegged back by Mohamed Salah, they managed to hold on for a point despite facing 35 shots and giving up 71% of the possession.
The result means that Burnley have now taken five points from away trips to Chelsea, Tottenham Hotspur and Liverpool this season, having ended the previous campaign with the second-worst away record in the league.
"I think you have got to defend well at these places. Our gameplan wasn't to come here and think, 'We are going to keep the ball all afternoon', but it is much harder to score from 30 yards than six and I thought we did [limit chances] well today - other than their goal," he told reporters.
"My job is to allow this team the best opportunity to be successful. We dropped one into midfield and had an extra one rather than 4-4-2, and I am really pleased with the game plan.
"Everyone says [Liverpool] are having a tough time with set pieces. We thought that would be important. We had two cleared off the line with set pieces, so our gameplan was right to make things uncomfortable for them."
Burnley stay above Liverpool in the Premier League table as a result of the point.