Violent scuffles broke out in the Millwall section of supporters during the closing stages of their 2-0 defeat to Whelan's Latics at Wembley.
Police were eventually sent in to try and restore order as the violence escalated, with the Metropolitan Police confirming four officers sustained "minor injuries".
12 Millwall fans were eventually arrested, while others were bloodied and younger supporters left in tears because of the violence that erupted around them.
The shocking scenes overshadowed Wigan's achievement in reaching their first ever FA Cup final and Whelan believes the perpetrators should be dealt with severely.
"I thought it was disgusting," Whelan told Sky Sports. "Their own supporters fighting with each other, what are they fighting about?
"If they are losing what they want to do is get behind the team, get behind the club and support them.
"Normally they are not like that. Hopefully the police will have got them and I think maybe they should put them inside for three to six months, quieten them down.
"You can't have a game of football where supporters are fighting, it's bad enough when they [two sets of fans] are fighting each other, but when they are fighting amongst themselves, like the Millwall fans, totally unacceptable."