Parry said he admitted that early results had possibly raised expectations to unrealistic levels, but that he believed Benitez would challenge for top honours soon.
He said: "For Rafa to reach a major final in his first season is a great achievement, and no-one at Liverpool would belittle that.
"At the same time, while there was a lot of guff written following our FA Cup exit, we will not be deflected from our primary objective which is success in the Premiership and Champions League.
He added: "It's the whole package and all the work he's done since he arrived. It's possible some of the results he achieved early raised expectations a bit too early.
"During the summer, everyone was talking about this being a season of transition and stressed how the new manager needed time. It seems to me this all went out of the window last week and suddenly we are in a 'crisis' again. The common sense had gone.
"The League Cup was a springboard for success in 2001 and gave the supporters a great day in 2003. Hopefully we can repeat that again."
