The 57-year-old lost his job on Sunday having lad the Owls to just one win in the Championship this season.
Wickham expressed his gratitude to the former Stockport County, Southampton, Wolverhampton Wanderers and Cardiff City boss, who initially took him on loan from Sunderland last term.
"Personally, I have got the utmost respect for [Jones]," PA quotes the 20-year-old as saying. "He brought me in and showed belief in me when maybe no-one else did last year, but we have to get over it.
"We had a game 48 hours later and the reaction we showed was top class. Our performances haven't been up to scratch, that wasn't down to the manager, so it is up to us to pick up from here and move forward.
"We've got a good bunch of lads and we know how to deal with these situations as a team. We showed everyone what we are capable of doing when we get our heads down and perform well."
The England Under-21 international joined the Black Cats from Ipswich Town for £8m in 2011.