On Thursday, Appleton confirmed his chairman Karl Oyston and the Barclays Premier League club had held discussions about Ince, who left Anfield with one senior appearance to his name last summer, but the initial fee put forward fell short of Blackpool's valuation of the England Under-21 winger.
Ince was one of a number of Seasiders players frustrated by a goalkeeping masterclass from Carl Ikeme as Wolves left Bloomfield Road with a 2-1 npower Championship victory thanks to a goal in each half from striker Sylvan Ebanks-Blake.
Asked after the game whether Liverpool had upped their bid, Appleton said: "No, not that I'm aware of."
On Ince's impressive individual display, he added: "It was important for him and he's got to show a strength of character now to suggest that, with everything going on, all he wants to do is play football and play well for Blackpool Football Club."
Blackpool dominated the contest for long periods after Ebanks-Blake found a cool finish in the third minute to ensure Wolves opened the scoring for the 15th time in 23 Championship outings this season.
But Ince and Portuguese playmaker Tiago Gomes could not find a way past the inspired Ikeme either side of half-time, while the latter also thudded a drive against the base of a post.
Ebanks-Blake netted from the penalty spot after Chris Basham pulled Bakary Sako's shirt and Appleton, who saw his skipper Alex Baptiste set up a grandstand finish by netting a late header, was unimpressed with the spot-kick award.
"You don't have to be a rocket scientist to weigh up the whole game and look at the opportunities we created in both halves and say we probably should have got something out of the game," he said.
"But it wasn't to be, a poor two or three minutes at the start of the game and we won't talk about the other decision."
- Sports & Recreation
- Blackpool Football Club
- Carl Ikeme