In Burnley' s 5,000th league game - becoming only the second club, after fellow Football League Founder Members Preston North End to achieve the feat - the Clarets came from behind to hold United, with Jay Rodriguez scoring his 100th career league goal.
Burnley trailed to a Paul Pogba goal, which came in between two disallowed United goals for Raphael Varane and a Josh Brownhill own goal, the first for off-side and the second for a foul.
But the crowd stayed with the Clarets, bottom of the table with only one league win this season, and new signing Wout Weghorst bamboozled Harry Maguire, before a superb reserve pass allowed Rodriguez to get his body in front of the hapless Maguire and sit David De Gea down before finishing.
Maguire could have seen red for hauling down Jay Rodriguez later on, but Dyche said: "We asked for a reaction and wanted that, and the fans played their part at half-time and stayed behind the players.
"And the players gave a reaction and the second half was pleasing and much more like we want to be like.
"In the end we have to be pleased with a point, it is only a point but it is a positive point.
"We are in a situation where we are bottom of the league, I don’t think we should be there but we are.
"It is difficult, we are playing Manchester United. There might be some noise about them, but you look at that teamsheet and there are some top players on there.
"We stayed intact and in the second half we just reminded them.
"I asked for a bit more from a few individuals in the first half because I thought we were carrying a few, and there was a really good reaction from every individual and the team.
"In the first half you could argue United were very good and we were slightly off, or we were off and that made United very good.
"The second half I was pleased with the quality of the play and demand of the players to take the game on."
Maxwel Cornet hobbled off late on, but is expected to be fit to face Liverpool on Sunday, and Dyche added: "We have to make decisions with Maxwel, I was almost not going to play him because of his fitness levels and the risk of injury.
"He is still adapting to the Premier League and has hardly played in weeks.
"His training schedule has not been the demand we have for the Premier League, so we are trying to factor all those things in and getting him fit and not break him. It is a fine line.
"He did fine and his fitness will improve and his sharpness will improve.
"I don’t think his injury is a serious one, it was more of a knock.
"But he was cramping up as well and fatiguing and he was definitely going to come off at that stage anyway because we have got to be very careful. We can’t keep losing players."