The pair noticeably embraced after victory over QPR on Saturday.
Pardew explained: "There was a reason for going on the pitch at the end of the game to see Colo.
"We fell out this week and we're entitled to do that - as the captain and the manager. I just said to him before we walked out on the pitch, 'Look, we are both winners, we are allowed to fall out'.
"It was just a silly little thing and I know he was determined to get the result.
"I said to him before the game, 'Be our leader today, be a captain and make sure they don't get a sniff of a goal'.
"And when you ask someone to do a job and they do, it's only right that you pay your respects to them.
"You fall out with players all the time as a manager, because if not, you're not doing your job.
"Sometimes I have to say what I think is right. Even your most senior players can disagree with that. I have no problem with that.
"I feel that in any walk of life you have to be a man sometimes and admit when you're wrong and also pay your respects when someone does something very right and I thought Colo was absolutely brilliant today."