With the score at 3-0 Mane, scorer of the second just before half-time, was substituted but apparently annoyed by Mohamed Salah’s failure to pass to him moments earlier and the Senegal international produced an emotional reaction on the bench.
Henderson, however, said he was pleased to see it – even if it was from the usually mild-mannered Mane.
“I’ve seen it now and again (from him). Sadio is fine, he’s a great lad,” said the England international.
“That’s just us pushing each other all the time. I think that’s important. We all want to do better, we all want to improve, but we’re really close and I think we can deal with that.
“I’m not sure (what set him off) to be honest. I couldn’t really understand at first but then when he came in, he was laughing and joking.
“The most important thing was we got the result, Sadio knows that. He performed really well again. Him and Bobby were really big second ball. He had a fantastic game.
“Like I said, we want to push each other. We want to improve all the time, I quite like that now and again. I think we need it.”
Having overpowered Arsenal last weekend this was a different type of performance, weathering Burnley’s early fire to grind their way through the tough passages before effortlessly moving through the gears when opportunities arose.
The breakthrough came from a Trent Alexander-Arnold cross which deflected off Chris Wood and ballooned into the top corner.
Their second was classic Liverpool: forcing the opponent – on this occasion Ben Mee – into a mistake with Roberto Firmino capitalising to release Mane for a well-taken goal.
Firmino became the first Brazilian to score 50 Premier League goals when he launched and finished an 80th-minute counter-attack.
It was a clinical and professional performance which extended the top-flight’s only 100 percent record to four matches and ensured they took a two-point cushion over Manchester City, who had briefly gone top having played earlier, into the international break.
For the first time in their history Liverpool have won their first four league matches in back-to-back seasons but Henderson insisted the standards they are setting were not considered by the players to be sending a ‘catch us if you can’ message to their rivals.
“We’re not setting them for anyone else, we’re setting them for ourselves. That’s what we want to do,” he added.
“We want to win every week, we want to perform every week and that’s difficult because there are so many good sides in the Premier League and in Europe. It’s really hard.
“Again for us, it’s game by game. We come up against different tests each week and it’s about giving everything every time we go onto the football pitch and we will see where we are at the end of the season.
“For me it’s just about concentrating on what we need to do. We have been very mature in our performances, especially away from home.
“We want to continue that form, keep doing the right things, keep working hard as a team. If we do that, we can put on performances like that.”
Burnley manager Sean Dyche was satisfied with the performance despite not having won since the opening day of the season.
He felt his players had to learn from the likes of Liverpool if they were to improve.
“I do think these and Man City are the best,” he said.
“If you turn the ball over in a bad area the number of times they capitalise on it and at least get a chance changes the mentality of the game.
“You learn from these top teams. When we worked in transition we didn’t find those killer moments.”