Christopher Mills, aged 25, and Ashley Stanton, 22, both of Walsall, pleaded guilty to racially and religiously aggravated harassment in the town centre on May 25.
It came three days after Mr Rigby was attacked and killed in Woolwich on May 22.
Walsall magistrates heard the pair had been drinking alcohol at Yates in Leicester Street when they began voicing their opinions. They were also waving St George flags.
Miss Indira Sharma prosecuting, said: "There were a group of around 10 to 12 men, and police officers were concerned that it was a possible EDL demonstration.
"They were concerned the situation could become inflamed because of previous EDL demonstrations in the town, but this was not one of them.
"The officers stayed outside of Yates public house where the men disclosed their views.
"They began walking to Crown Wharf while chanting 'this is England' and words inciting religious hatred."
Miss Sarb Sehmi, defending Stanton, said he had been drunk at the time of the offence and could not remember what he had said.
She added: "When officers told him what he had said, he could not believe it. If he had not been drinking he would not have been in court.
"He is going to the doctors to seek help for his drinking and currently lives with his nan, who he supports. He also has two children who he supports financially through his job as a window fitter."
Mr David Houldcroft, defending Mills, said: "The men were opposed to the killing of Lee Rigby and they had been drinking.
"Mr Mills joined in with the group chanting stupid things but he apologises and says he is not a racist."
Stanton, of Bickley Road, was ordered to pay a fine of £670 by district judge Michael Morris.
Mills, of Cartbridge Crescent, was told to pay £710. An extra £40 was added to his costs after he failed to turn up to court on time.