Swansea magistrates said Robert Riley's online messages were also racially and religiously aggravated and that only a custodial sentence could be imposed.
Riley, from Port Talbot, was sentenced to eight weeks in custody after admitting posting an abusive Twitter message about the death of Leeds schoolteacher Ann Maguire.
The 42-year-old was the second person to be charged with the offence in the wake of the death of Mrs Maguire, who was stabbed to death in her classroom at Corpus Christi Catholic College last month.
Yesterday a third person was arrested in Cardiff and bailed.
More top news
Although there may be a crucial Euro 2016 game in Paris tomorrow afternoon another topic is overshadowing France's capital.
Holyhead is one of Britain's busiest ports, but after today's vote what does the future hold?
David Cameron has announced he is to resign as prime minister by October. We look at who could replace him.