United were well in the match at the break, 2-1 down, but Riyad Mahrez’s strike with just over 20 minutes seemed to completely deflate the visitors.
They had just 8% of possession in the 15 minutes that followed as City passed the ball around with ease, before Mahrez added his second in added time to give City a dominant 4-1 win on derby day.
Roy Keane was among those who slammed the United players after the match, but Rangnick took encouragement from his side’s display in the first 45 minutes, even if they then struggled badly as the game went on.
“I think we played a good first-half,” Rangnick said.
“We were competitive in the first-half. Obviously difficult to concede an early goal. We came back, scored a brilliant goal ourselves and had our moments in the first-half on the counter-attack.
“Then we conceded another too easy goal, and the second-half from the moment they scored the third one it was a very difficult game against one of the best teams in the world in possession of the ball. If you keep chasing the ball, you concede probably a fourth, fifth and even sixth goal.
“We conceded a fourth in the last minute of the game. It was a difficult day that shows we have some steps to go to close that gap.
“For us it was clear if we want a chance to win the game we have to do a lot of running. You have to be in attacking and hunting mode and we did that in the first-half, the players tried everything. The third goal killed us off in the end.”