The Lions bowed out of the competition on Saturday, with Shaun Maloney and Callum McManaman scoring the goals which booked Wigan a place in the final.
During the second half a group of around 20 Lions fans began fighting among themselves.
The Football Association has launched an immediate inquiry into the "deplorable" scenes while Millwall have vowed to ban those involved.
And Shittu said: "No players want that to happen. It was supposed to be a happy day, regardless of the result it was meant to be good day out at Wembley.
"I'm disappointed by it but as players we just have to keep doing what we do.
"At the end so many supporters showed they were there just to spur us on but it's disappointing to hear about such things happening on a day like that.
"It's a small minority but things like that should not be happening. It should have been a great day for both sides."
Defender Shane Lowry added: "Sometimes you get a minority, but we brought almost 32,000 fans and the majority were fantastic. They out-sung the Wigan fans and backed us throughout the whole game.
"It's disappointing to see incidents like that but the majority of fans have been fantastic this season."