Daniel Sturridge replaces Sadio Mane in the front three, with the Senegal worldwide serving the first of his three-match ban.
Klopp made seven changes from the frustrating mid-week draw with Sevilla, and having received a warm reception from the Anfield crowd as a substitute that night, Philippe Coutinho made his first start since attempting to force through a move to Barcelona.
Mohamed Salah's 30th-minute goal ensured the points were shared against Burnley, who took the lead three minutes earlier through Scott Arfield, and Klopp attempted to ease the concerns of supporters who are still reeling from Liverpool's 5-0 defeat at the hands of Manchester City in their previous Premier League outing.
"I think we are a completely different outfit now - the experience we have on a personal note and as a team and a club".
The loss dropped Liverpool to eighth in the league table, but they are only three points off leaders Manchester United.
Sean Dyche's side nearly claimed all three points as they managed to gain some territory late on, with Ben Mee seeing powerful headers from consecutive corners cleared off the line in the final 10 minutes, first by Matip, then goalkeeper Simon Mignolet.
Burnley, of course, have already won 3-2 away at Chelsea this season.
"We put that all together into a performance today and got something from the game". We made seven changes but we were still really fluent, offensive football, dominant football.
Liverpool fans react to Coutinho display against Burnley
Chance after chance fell Liverpool's way - headers going narrowly wide. "A lot of parts of the game I was really happy with". But from his point of view it will be great for him to get some club football under his belt going into the worldwide games.
"Then when the players got their drinks, he said it was maybe a bit of cramp so we thought it was maybe better to bring him off".
Coutinho was replaced by Solanke after a sub-par performance, with U/20 World Cup player of the tournament nearly turning one point into three, but he contrived to hit the woodwork with the goal gaping as the match finished 1-1.
The goals opened up what had been a tight affair with Salah, twice, and Sturridge testing Pope with low shots that were comfortably dealt with.
"Second-half, when you really need your keeper he makes two great saves".
"Now we have to use this quality consistently".
Heaton joined northwest side Burnley in the summer of 2013 and had played every league game in each of his three seasons before the last term, when he only missed three. It feels unusual, it feels wrong, but it's a fact - we drew.
His excellent save from Trent Alexander-Arnold drew applause from Klopp, while another stop, pushing the ball onto the crossbar from Dominic Solanke's header late on, proved to be a game-saving intervention.