The defender is off contract in June and saw a move to Wigan Athletic on deadline day last month fall through.
Simpson said: "It's been a tough few months but I've got a good relationship with the manager who knows my situation with the club.
"I'm the type of player who trains hard no matter what's going on. I think the manager might have seen that and maybe that's why he gave me the nod in Kharkiv. It was good to repay him by playing my part in getting a win.
"We've brought in players the club needed and they've settled in really well, they're quality players. Hopefully I've staked a claim a little bit or at least given him something to think about. It's massively important for me.
"I've got through a tough game so if I can keep training hard, hopefully the manager will pick me.
"I'm a professional footballer and I'm a Newcastle player now. There's three months to go and all I can do is train hard every day.
"I said to the manager whatever happens - injuries, suspension or whatever - he can rely on me if he does need me. That's all I can do, concentrate on training, and if I do get picked for the Europa League I've got to perform. Once the manager picks me and I'm on the pitch it's up to me to show what I can do. We'll just have to see in the summer what happens."