Antonio Conte’s side are lagging nine points behind leaders Manchester City after losing their last two league matches.
The Blues, who host Roma in the Champions League on Wednesday, crashed to a shock 2-1 defeat at lowly Crystal Palace on Saturday, an embarrassing setback that followed a damaging 1-0 loss to City at Stamford Bridge.
With title contenders Manchester United and Tottenham also in good form, Alonso knows Chelsea are in danger of losing touch with the early pace-setters.
Recalling Chelsea’s 13-match winning streak which followed losses to Liverpool and Arsenal early last season, Alonso said he believes the Blues need to be even more consistent if they are to catch City.
“We’ve lost a lot of points already. We cannot lose any more games,” Alonso told reporters on Tuesday.
“It’ll obviously be very hard. There are teams playing very good football and there are so many games still to come.
“So we have to think game by game. We will focus now on the Champions League, an important game, and then have time to get ready for Watford and the Premier League on Saturday.”
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