United failed to make the most of their first-half dominance at Turf Moor, where they had two goals disallowed either side of Paul Pogba’s first league strike in over a year, and paid the price as Jay Rodriguez brought Burnley level two minutes into the second half.
It was an all too familiar pattern for United – Rangnick’s side were knocked out of the FA Cup on penalties by Middlesbrough on Friday night but should have been out of sight by half-time, three weeks after they blew a 2-0 lead to draw at Aston Villa.
The result saw United slip to fifth in the Premier League as West Ham edged out Watford 1-0 to climb above them, and they could drop further on goal difference if Arsenal beat Wolves on Thursday.
Rangnick was upset by the disallowed goals on Tuesday, particularly the second – an own goal poked home by Josh Brownhill but ruled out after Pogba and Erik Pieters tangled in the build-up – but he acknowledged United needed to do more.
“We should have been at least 2-0 up at half-time,” Rangnick told MUTV.
“But we said the same after the Middlesbrough game. We were doing extremely well on the ball and controlled the game but in the end it’s about winning the game.
“Today with only one point after those 94 minutes, nobody can be happy. And above all, if you want to be fourth in the league, we should not lose points like the ones tonight.”
Burnley emerged for the second half a different side and drew level through Rodriguez’s 100th career league goal and first in 50 league appearances.
Wout Weghorst then brought a fine save out of David De Gea as Sean Dyche’s relegation-battlers threatened to make it worse for United.
“The second half we didn’t start well, we were not aggressive enough, we were not composed enough on the ball,” Rangnick added.
“Even the two minutes before we conceded the goal, three times we had won the ball and played tiki-taka football in our own half and gave away the ball too easily.
“Then we had our own counterattack, 20 seconds before they scored. The behaviour of our team in those 10 seconds before they scored was just not good enough. We had two or three players in our own half but still allowed them to score the goal.”
Burnley had been booed off after Saturday’s goalless draw against fellow strugglers Watford left them rooted to the foot of the table, but there was a different atmosphere on Tuesday.
There was a huge roar of encouragement as they went in behind at the break, and the fans got their reward with the second-half performance.
“I thought the fans were excellent all the way through,” Dyche said.
“Man United were the better side in the first half, we never got to grips with our performance. Obviously they are a good side but we never got near what I was hoping for other than the work ethic of the defensive unit.
“But we made a reaction and the fans played their part in that. They stayed calm, they stayed behind the players and the players gave a reaction. That was much more like what we want to be like against a very good outfit.
“Yes, it’s only a point but it is a very positive point.”