Kompany, who only signed from Hamburg last week, told Sky Sports 1: "I just loved it. I enjoyed it 100% - lots of duels, lots of energy.
"I've got to be honest, I signed two days ago, trained once and today I played and didn't know their names.
"During the game I learned their names, learned how everyone plays.
"It was a lot of fun. I wanted to play an intelligent game and try to do my best for the team."
Belgium international began the match in midfield but dropped back to centre-half when Richards went off following a collision with team-mate Tal Ben Haim.
"I loved it in midfield but a job had to be done in defence," Kompany added.
"That's why the trainer (manager Mark Hughes) took me, because he can count on me in different positions.
"I'm just happy with the result."