"We understand the expectations at Liverpool but we are clearly moving in the right direction under Rafael Benitez," said Parry on the club's official website.
"We unquestionably have a better squad than we did last year so it is not about making judgments at this stage. There are no trophies handed out at the end of October, with the exception of the Community Shield which we have already won. You can only judge our performance over the course of a full season.
"We all knew there was a sizeable job to do when Rafa was appointed and that is why we have never laid down any timescales or imposed unrealistic pressures. What is important is continuous year on year improvement.
"The wins in Istanbul and Cardiff were great achievements which we celebrated together. Some of the early results in the league have not gone as well as we would have wanted which is why we have a collective responsibility to pull together and work even harder to improve things on the pitch."