The Premier League club got the better of FC Gomel 3-0 on Thursday in style, thanks to goals from Fabio Borini, Steven Gerrard and Glen Johnson.
The win saw Liverpool progress to the play-off round of the Europa League, leading Reina to express his faith in Rodgers’ footballing philosophy.
“It was a good night’s work,” the Spain international told the club’s official website.
“We kept a clean sheet and got the result, played well, got through, and I’m happy for the fans.
“It’s always enjoyable for me when the team wins, especially when we keep a clean sheet. That’s the way it should be in almost every game, especially at home.
“It’s coming along little by little. We have to be patient. It will take time – it’s not a four-week project. We want to create our own style of play and that will take a little longer than four weeks.
“All we ask from the people is to be patient and have trust in the team because I think we are going to come good.”
Glad to be back
Reina was part of the Spain squad that successfully defended their European Championship title last month, and was given an extended break by Liverpool.
However, the 29-year-old insists that he is glad to be back in action for the Reds.
“I’m always happy to come back. It’s been a busy summer – a happy, but busy summer – but it’s great to be back,” added Reina.
“I’m looking forward to the start of the season and hopefully we can continue to keep getting positive results at Anfield.”
Liverpool will host Bayer Leverkusen in a pre-season friendly on Sunday.