After Sunday's match, which City won thanks to goals from James Milner and Edin Dzeko, TV footage picked up Brooks telling the City players 'they’ve paid 62 quid over there, go and see them' as they exchanged handshakes following the final whistle.
Kevin Parker, general secretary of the Manchester City Supporters Club, said: "This is such a shame. All football fans want the officials to be human and show empathy and something like this sends the wrong message.
"The linesman was having a private conversation with one of our players. From what I can see, he was being a normal, sympathetic human being, rather than a robot.
"All the people I have spoken to — City fans and fans of other clubs — thought it was a great thing to do."