The pressure was increased when Ashley Westwood scored straight from a corner, but Roberto Firmino and Sadio Mane each netted twice to secure the comeback, despite a late Johann Gudmundsson goal amid hard conditions on Merseyside.
And the German manager, whose side visit Bayern Munich in their Champions League last-16 second leg tie on Wednesday, insisted that the performance demonstrated his team's ability to handle the pressure.
The report explains: "The Spanish giants are looking to shake up their defensive options this summer - and Liverpool are taking no chances with their £75 million star, who has been a driving force behind their Premier League title bid".
"It's not about us making excuses, because we don't. We are in a good moment".
Lallana's charge down of Jack Cork's clearance meant the ball broke to Mohamed Salah in the box.
"With how we play, there can be a lot of chaos going on, with counter-attacks and when we win the ball we go again and go again". The counter press is a game-changer.
"It didn't look really promising until Adam jumped in, so well done, (I'm) really pleased for him".More news: Lakers pausing Melo talks unless team turns season around
For Burnley, Steven Defour has undergone surgery while Aaron Lennon is out with a knee injury with both players unavailable for the clash.
When Ashley Westwood scored direct from a corner into the Kop end goal after just six minutes, fears that Liverpool's title jitters were about to get worse were raised.
"Usually it would have been disallowed, if the ref had a better view, I don't know exactly". You can not treat the goalie like that in the six-yard box.
"The good thing is it was early, so we had enough time to react, to turn it around".
- Liverpool's tally of 73 points from their opening 30 league games this season is their joint-best ever total at this stage of a league campaign (adjusting to three points for a win), level with the 1904-1905 second tier season and 1987-1988 in the top-flight.
Belgian worldwide Lukaku scored two goals to give Manchester United a priceless 3-1 win at Paris Saint Germain (PSG) in their last 16-second leg clash and that was more than enough for the Red Devils to secure a quarterfinal spot on away goals.
Firmino then added another with a little under 25 minutes to go, before late drama saw Burnley pull a goal back via Johann Gudmundsson.