Aberdeen defender Anderson and his team-mates are in confident mood ahead of their season opener against Kilmarnock tomorrow.
However he told the fans that the players are not going to get carried away by the 'favourites without Celtic' tag given to the Dons by bookmakers.
Anderson said: "I can see why they're making those predictions, but they made the same predictions last season and look what happened.
"I think it would be foolish to start shouting from the rooftops we're going to do this, we're going to do that, because, as last season showed, things can quickly unravel.
"We had a good start to the season, but we tailed off. For the new players coming in, this is all new to them and I'm sure they'll be feeling confident as we all are going into the start of the season, but we're not going to get ahead of ourselves."