Chelsea's cushion to the chasing pack now stands at just one point follow Monday night's defeat to Manchester United - their third in all competitions against the Red Devils this season.
Frank Lampard's side are fatigued and faltering after a flying start to the season, even with the winter break recently restoring some energy.
Jose Mourinho returns to Stamford Bridge with fifth-placed Tottenham on Saturday knowing a win or draw would see his former club drop out of the top four.
"We are still fourth so we are still in a good position but we need to wake up because they are coming from behind," said Kovacic.
"We need to play these next games like we were playing in the beginning of the season and change some things as well, obviously.
"We need to improve a lot because we have tough games ahead of us and we have to be focused.
"We have to train hard every day, to prepare our games better and try to avoid our mistakes because we are making too many mistakes in these kind of matches and you get punished.
"We have a good week ahead of us to prepare for Tottenham and to play a good match. We know this match means a lot for us because Tottenham are close behind us so we need to prepare ourselves quite a lot to win this game at home."
As has so often been the case with Chelsea this season, they dominated proceedings against United but wasted golden opportunities and were punished by sloppy defending and more clinical finishing.
Michy Batshuayi was given a chance to show Lampard that he was right not to sign striker last month as the Belgian came in for the injured Tammy Abraham.
However, on just his fifth Premier League start for Chelsea, the striker wasted a wonderful opportunity in the first half and struggled to lead the line with any authority before being replaced by Olivier Giroud.
The Frenchman showed more promise but had a first League goal of the season ruled out for offside after a VAR review.
"We played well in the beginning but it’s always the same against United - we play good, we create chances, we don’t score and then they score from one opportunity," Kovacic told Chelsea TV.
"We don’t have the three points and that’s the most important thing. It was a good game from us, we played well, like we have for more or less the whole season, but we made some silly mistakes and we lost the points.
"We are still a very young team and we need to improve a lot. Now we will see if we are a great team because we have some tough matches to fight for the fourth position and we need to show ourselves."