Ruben Neves earned Wolves a 1-1 draw with a magical strike from the edge of the box, before Rui Patricio saved Paul Pogba's penalty to keep the scores level.
Coady said Wolves believed they could win the game – but was happy with the desire they showed to earn a point.
“It is important to have that type of grit and bite," he said.
“We found it tough first half to get out, they pressed us really high and really fast.
“I thought they came with an intent to do that and they played well.
“But the manager spoke at half-time fantastically well like always and showed us a few other things we needed to do.
“We managed to get to grips in the second half. We pressed them a little bit higher and kept the line a little bit higher.
“We managed to play out past the press a little bit better as well.
“That was something we needed to do because when you have a team like Manchester United coming here you have to get to grips with them as soon as possible.
“I think it was important we went in not conceding two at half-time which made us stick in there.
“Second half I thought we were brilliant, especially at the start."
That's the third Premier League game in a row against Manchester United that Wolves have fallen behind – but on each occasion they have battled back to earn at least a point.
“We have some fantastic footballers but more importantly we are fantastic friends and we all stick together," Coady added.
"We are close to each other and we make sure we never ever give up.
“You have seen that tonight because Raul (Jimenez( was so unlucky with the header he had but we scored the goal just after which was brilliant.
“It is something we need to make sure we keep in our game for as long as possible because it is important."