Liverpool have taken just six points from their opening six games and currently sit just two places above the relegation zone, with Hodgson struggling to turn things around after replacing Rafael Benitez this summer.
Reina is confident that Hodgson's methods will prove successful at Anfield, but he has warned Reds fans not to expect too much in the short-term.
"When you have so many changes moving in a new direction under a new boss, things don't happen instantly," he told LFC Weekly. "It can take between three and six months before you see improvements.
"Obviously, the quicker we adapt and improve as a team, the better it will be for everyone. That doesn't just happen overnight. Each of us has to adjust to working in a new way.
"With the passing of each day, I get used to it and what the manager wants. It's the same for all of us. We need to be patient."
Reina feels, though, that Liverpool have not been helped by the fixture list at the start of the season.
"People who criticise us about it should look at the fixtures we've had. It has been a difficult start. Arsenal at home and then going to play Manchester City, Manchester United and Birmingham away was never going to be easy.
"Not many teams will go to the City of Manchester Stadium, Old Trafford or St Andrew's and win. Those three teams have very good records at home."
Meanwhile, Hodgson is warning that Fabio Aurelio could still be some way away from a first-team return after suffering an Achilles injury last month.
"Where Fabio Aurelio is concerned, caution and prudence have to be the words that we use," he said. "He is progressing all the time and his efforts are very commendable but we can't bring him back too early.
"We took him off against Trabzonspor as a precautionary measure, as we didn't want to run the risk of him sustaining a serious problem."