The Seasiders saw their Capital One Cup campaign collapse at the first hurdle on Monday, as they suffered a 1-0 first round defeat at local rivals Preston North End.
Ince, who turned down a move to Cardiff City earlier in the summer, was once again involved at Deepdale.
It remains to be seen how many more times the England U21 international will turn out for Blackpool, with the transfer window ticking down, but father Ince hopes he can focus on making additions to his ranks over the coming weeks rather than worrying about departures.
Asked if he would like to see his son remain at Bloomfield Road for the entire 2013/14 campaign, he told Sky Sports: "It would be nice. It would be nice to keep him, obviously.
"He's a quality player and there has been plenty of interest for him, but it just shows how thin we were on the ground today.
"We have had to play more or less the same team from Saturday. Two high intensity games - Doncaster away on Saturday and then a derby here. It just shows how light we are on the bench and how light we are strength-wise.
"We didn't really want to play (Michael) Chopra and (Steve) Davies for 90 minutes but we had to keep them on because, attacking-wise, we are short."
Preston boss Simon Grayson added: "The result shows everybody what it means to the football club.
"I thought it was a cracking cup tie with a great atmosphere with some good football and good defending.
"We played with great shape and organisation and worked hard, passing the ball when we could in what was a tight game."