"It is a hard job the referees have. I was wrong to do that," Moyes told the BBC.
"I thought it was a free kick on Leon Osman on the edge of the box in the 92nd minute by (Frank) 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."
Manchester United manager Alex Ferguson was criticised for his outburst at referee Mike Dean during his team's 4-3 win over Newcastle United last week.
The United boss was fuming after Dean awarded Newcastle's second goal, over-ruling his assistant who had flagged for offside.
When Dean came out for the second half of the match, Ferguson, who escaped FA punishment, followed the referee on the pitch, venting his fury.
(Reporting by Toby Davis; Editing by Peter Rutherford)
- Sports & Recreation
- Mike Dean
- Leon Osman