Sunderland’s Texan owner has also announced that he has talked to manager Martin O'Neill about summer transfer targets, and says they will be shopping for quality, not quantity.
"There is a lot of pressure, not just to stay in the Premier League but to improve," Short told Sky Sports.
"We are not happy with finishing 13th, we are not happy at all but we realise that you need steady progress, you need continual progress.
"You don't want to finish seventh twice in a row and get relegated the next season, which has happened in the past.
"We do feel like now with Martin and with the progress we have made, we are well-positioned.
"We want to be well within the top ten - we certainly can't promise that but we are not happy with where we are and we do want to continue to improve, and yes, there is huge pressure to do so, both from the fans and their expectations and also just from the sheer size of the economics that are involved in the Premier League.
"He [O'Neill] and I have been talking all summer long about what we are going to do.
"The fans have a pretty good idea of what we need to do and everybody has a pretty good idea of what we need to do, so now Martin is looking at specific players that we might want, and then there will be a lot of work and then trying to get those players here.
"But we don't want to sign players just for the sake of signing them, or because it feels like they are inexpensive for some reason.
"We want to identify players who are good and who will definitely improve us, and try to bring them in."