Vialli made the comment in his role as a pundit for Sky Sports Italia during Chelsea's 3-1 defeat by Tottenham Hotspur on Sunday that left Conte's team eight points behind Spurs in the race to secure Champions League football next season.
The Blues have put up a measly defence of their Premier League crown and now sit 11 points adrift of Tottenham Hotspur, who occupy the final Champions League qualification spot.
Conte also said Chelsea need to be "realistic" about their chances of qualifying for next season's Champions League. We have to try to give all ourselves. "But this is the moment we have to face with the greatest desire to change the situation".
"We are not clinical". We must be focussed on the present and go game by game.
"We have to improve, we must win this game".
"I think with this game, we can see our season", Conte told the BBC. "He is a great player and will probably leave one day for a high fee, but I wish him to stay with us for a long time".
"When this happens regularly and you stay in this position, it means you have problems". He has been linked with many teams who are in pursuit of a good manager. This is the truth. A lot of times.
But it was a disappointing conclusion to a miserable week for Chelsea, who were mourning the death of their former star Ray Wilkins.
Fans placed shirts and scarves at a temporary memorial outside the ground and queued to sign a book of condolence in honour of Wilkins, who suffered a heart attack last week and passed away at St George's Hospital in Tooting on Wednesday morning aged 61.
Despite enjoying 60% of possession and tallying up 23 shots, only six of Chelsea's efforts were on target, with Alvaro Morata seeing two goals chalked off for offside and Willian missing two sitters.
Moyes had special praise for striker Hernandez and goalkeeper Joe Hart.
Antonio Conte disputes this idea as well, claiming he wants to see out the the third and final year of his contract.
Before Chelsea's fixture against West Ham today at Stamford Bridge, a video was shown from the big screens at the stadium.
And in the 73rd minute Marko Arnautovic collected Gary Cahill's weak headed clearance and cut the ball back for Hernandez to slot home.
'Chelsea were really good in the first half but we kept it to one, the goal we lose is dire, I could accept conceding from some of their great play but the goal was so poor.
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