Scott McTominay won the match with two goals in a dominant display for the Red Devils and a 2-1 scoreline which flattered the Blues.
Cole Palmer equalised just before half-time but Bruno Fernandes had earlier missed a penalty and watched his team-mates see a number of later chances go begging.
After an important win, which puts United just three points behind fourth-placed Manchester City, Ten Hag said: "It never felt like a crisis for us.
"We keep calm and trust the process. We’re in the right direction and need not to be distracted with things around us. We’re critical of ourselves and want to put things right and make it better. This team can be successful.
"You have to be a team, cooperate. Need good communication in and out of possession. Then you play well because we have a lot of great players. I know we can not play great every game because we are not robots."
Ten Hag praised Antony, who he believes is "progressing", and added on McTominay: "He’s a very good finisher. Sometimes he is deep and sometimes lower, but in our plan, we want him to be up there, and the team has to make that happen so he’s around the striker and make the runs.
"He’s got the smell. It’s a matter of organisation. We need players in the right position."