Henderson, standing in as captain for Steven Gerrard as he works his way back to fitness from a hamstring injury, opened the scoring just before the half-hour with a neatly-taken strike and then provided the cross for Daniel Sturridge‘s header early in the second half.
“It was a great strike and that gave us greater confidence in the game and his ball for the second goal was terrific,” said Rodgers. “He has great technique and precision and it was a great finish by Daniel.
“He is improving all the time and as he matures even more tactically he will become even better.
“He has always had athleticism, he is born with a natural gift to run, and tactically he is improving all the time and his passing is improving and he is becoming one of the real leaders of this team.
“It was a wonderful performance by him and the team in general.
“We controlled the tempo of the game and whatever we had to deal with defensively we did.
“As good as the performance was at the weekend (a 2-1 win over Manchester City) this was equally as good.”
Burnley boss Sean Dyche had no complaints about the result, which leaves his side next-bottom three points from safety.
“They (Liverpool) were very good tonight. They are an expensively-assembled side with top-class players who have found that run of form and belief,” he said.
“At 1-0 you never know but second half we gave away a really poor goal – the first one can happen with high-quality players.
“It is a different side to the one we played on Boxing Day. They are right in the zone and high on confidence.
“It is possibly too late for this season but if they carry on that you have to fancy they will be up there (challenging for the title) next season.
“We knew it would be a stern task to come here tonight to get a win but we keep learning. We have a 10-day window to put it back together.
“We will be relentless all the way down the line.”