England's Marcus Rashford, Jadon Sancho and Bukayo Saka, who are Black, were bombarded with online abuse after they missed spot-kicks in a penalty shootout with Italy which settled the July 11 final after the game at Wembley finished as a draw.
The Crown Prosecution Service (CPS) said Scott McCluskey, 43, from Runcorn in northwest England, had posted racist and insulting comments about the three players on his Facebook account.
McCluskey said he had been smoking cannabis and deleted the comments after other Facebook users objected to them. The racism and fan violence at the final at Wembley badly marred an otherwise successful tournament for the young national team.
McCluskey was sentenced to 14 weeks imprisonment, suspended for 18 months to oversee his behaviour. He must do 30 days of rehabilitation and be subject to an electronically-monitored curfew for much of the weekend, for 40 weeks.
He must also pay the victims £100 ($138) in compensation, costs and a victim surcharge.
"Hate crimes such as these have a massive impact on players and their mental health," Elizabeth Jenkins, CPS national lead on football, said.
"The CPS takes this kind of offending very seriously and this case shows that where offensive content is reported to the police we can successfully bring offenders to justice."