The champions came from behind to win 2-1 at Luton on Sunday but did so without injured top-scorer Erling Haaland, who was out with a stress fracture in his foot.
The 23-year-old, who has scored 19 goals this campaign in addition to the 52 he netted in his debut season at City, is also likely to miss Wednesday’s Champions League trip to Belgrade to face Red Star and Saturday’s meeting at home to Crystal Palace.
In-form winger Jeremy Doku also sat out the win at Kenilworth Road with a muscular injury, joining long-term absentee Kevin De Bruyne among those unavailable to manager Pep Guardiola as his team looks to chase down a four-point gap to league-leaders Liverpool.
“Obviously we missed key players like Erling and Kevin, it’s never easy when you miss such big players,” said Kovacic. “But they are not in the moment here, we need everybody to give 10, 20 per cent more like we did (on Sunday) and then we can win games.”
Defeat to Rob Edwards’ side would have left them seven points adrift of the Reds, but victory against Palace will move them to within a point of the top with the sides above them not playing until Sunday.
Bernardo Silva and Jack Grealish each scored in the space of three second-half minutes to turn the game around after Elijah Adebayo’s goal at the end of the first period had left them facing a fifth straight winless game.
“The team was confident because we were playing good,” said Kovacic. “We had not bad results, some draws where we could have won.
“This is football sometimes, then it’s about how you come back. Today we came back in a good way.
“A big three points. We showed overall great football, especially in the first half we played very well, we found a lot of players in the pockets which is what we want.
“When you do your thing and insist, the goals come. We could have scored even more, but I’m happy with the three points.
“We saw in recent games that big teams can struggle here. We showed that even when the circumstances are like this we can do our best and play good football.
“This team has shown over the years that in the tough moments, they are there, and they were there again (on Sunday).”