Speculation has linked Ince and Baptiste with being on the brink of joining Liverpool and Leicester respectively.
But Appleton had no qualms cup-tying the pair as he saw his side earn a draw after Ludovic Sylvestre's opener was equalised by Giorgos Karagounis' late strike.
"I certainly hope they will stay," he said.
"To me, they did not look fazed about anything going on off-field."
He added of Ince: "He is going through an indifferent period because of all the speculation but he is coping with it really well.
"I know how difficult it can be, so he has to take credit for that and I am sure that once the speculation settles down, his performances will pick up again.
"Liverpool made an offer two weeks ago but we have not received anything since. It was a case of, 'That's not enough. You'll have to do better if you want him'.
"Until that changes, he will stay here."
Appleton admitted he would have taken a replay before kick-off.
"It was their strongest side, so I am pleased to come away and still be in the hat and have the chance to bring them down to the Bloomfield Road cabbage patch," he said.
"It is as bad a surface I have even seen in the league. I don't think Fulham will be comfortable or enjoy playing there.
"We have to make sure we put on a performance because they are still quality."
Blackpool's goal, finished emphatically by Sylvestre, demonstrated their own quality but it was completely upstaged by Karagounis' wonder strike.
"It took a fantastic goal to get them back into the game," Appleton said.
"I asked the players to enjoy their defending because we knew that they would be doing a lot today.
"But they did well and didn't panic when Fulham started putting balls into the box and we put our bodies on the line."