Celtic have not won a league game on the road since February and lost again away from home on Sunday when Livingston beat them 1-0 at the Tony Macaroni Arena.
It left Celtic sixth in the league table and four points away from league leaders Rangers in the Scottish Premiership standings.
Rice believes Celtic are being judged by the standards of attacking football they set at home in their three league games at Parkhead where they played scintillating attacking football.
He feels the performances raised the expectations of the fans but stressed that Celtic at home are a completely different beast compared to the team away from home.
The former Hamilton boss insisted that Celtic need to find a way to mix and match away from home and stressed that they have to sometimes win games by not playing the prettiest football.
Rice said on the Go Radio Football Show: “When I look at Celtic, the standards they set in their three home league games, expectations of the fans rose very quickly.
“The new manager comes in, nobody knew much about him and all of a sudden they were scoring goals against Ross County, Dundee and St. Mirren and that set the standards and the expectations.
“Celtic are a different team at home, they are dynamic and they are quick on the break but it’s a different game when you go to Livingston.
“The pitch, the opponents, the way they set up and Celtic have to overcome that.
“You have got to win games ugly sometimes.”
Celtic’s next assignment is a Scottish League Cup quarter-final when they host Raith Rovers at Paradise on Thursday night.