The Blues have been left reeling after losing 1-0 at Manchester City to slump to their fourth defeat in five league games.
Conte's flops have gone from Premier League champions to 'chumpions' and now face a losing battle to secure a top four finish.
Conte is locked in a desperate scrap to avoid the sack as billionaire owner Roman Abramovich loses patience with the failing Italian.
Now Alonso has turned the screw on Conte even more by claiming there is an attitude problem in the dressing room.
The Spanish star said: "The team had the conditions and quality to play much better (at City) - and I don't think we were at our best.
"I think it's an attitude problem and we have to make things clearer and improve quickly, because we have nine matches left and we want to be in the top four.
"I think that it is difficult, but we have to change the attitude, right?
"I don't think we have a problem with quality, we have shown in many matches this season that we can be competitive against any team, like we were against Barcelona a couple of weeks ago.
"If we don't reach that kind of level of performance in every match it's because of our attitude."
Alonso has also twisted the knife into Conte by revealing his admiration for Luis Enrique, who is the red hot favourite to be the next boss at Stamford Bridge.
The Chelsea star added: "I don't know him very well in truth. But yes, without doubt, for sure (he is a good coach).
"With (what he did with) Barcelona he has shown that he is a good coach."