Everton manager David Moyes apologised to referee Howard Webb after confronting the official at the end of
Moyes waited for Webb to question why he didn't give an injury-time free-kick for a foul on Leon Osman.
"It is a hard job the referees have. I was wrong to do that," Moyes said.
Manchester United boss Sir Alex Ferguson was criticised for confronting referee Mike Dean during his team's 4-3 Boxing Day win over Newcastle.
Ferguson, who had been angered by Dean's decision to overrule his assistant and allow Newcastle's second goal, escaped Football Association punishment for his prolonged protests at Dean and his assistants.
Ferguson emerged for the second half of the match still in deep discussion with Dean about the 28th-minute goal.
Newcastle boss Alan Pardew suggested afterwards that Ferguson should have been dismissed for his outburst,
Moyes confirmed that he had sought out Webb after reflecting on his own behaviour.
"I thought it was a free-kick on Leon Osman on the edge of the box in the 92nd minute by Lampard and he didn't give it," he added.
"I've apologised to Howard Webb afterwards because I shouldn't do that coming off the pitch."