Kruse, who won 14 Germany caps between 2013 and 2015, was left out of Wolfsburg's 1-0 win over Europa League champions Eintracht Frankfurt on Saturday – their first Bundesliga victory of the season.
Both Kovac and sporting director Marcel Schafer declared there was no way back for Kruse, with the former saying: "We demand 100 per cent identification, concentration and focus on Wolfsburg from all players. We didn't have that feeling with Max."
Schafer then insisted the 34-year-old, who scored seven goals in 14 appearances for Wolfsburg last season after arriving in January, would not play for Die Wolfe again.
In a video posted on his Instagram account, Kruse refuted Kovac's claims regarding his lack of application, saying: "I respect the coach's opinion, apparently I should no longer identify with the club.
"But everyone who knows me knows I've been a professional for the last 10 or 12 years, when I always gave my all for the club I played for.
"That will continue to be the case as long as I get to train and play football.
"I came to Wolfsburg in January to help the team, and I think I did that in the second half of last season.
"I decide for myself when my time in the Bundesliga is over, and nobody else decides that for me."
Kovac and sporting director Marcel Schafer said on Saturday there was no way back for 34-year-old Kruse with the Bundesliga outfit.
Wolfsburg won 1-0 at Eintracht Frankfurt on Saturday, getting the better of last season's Europa League winners thanks to Maxence Lacroix's header on the hour mark.
It was a first victory of the Bundesliga campaign at the sixth attempt. Former Werder Bremen and Borussia Monchengladbach forward Kruse was left out, a week after playing the full game in the 4-2 home defeat to Koln.
"We demand 100 per cent identification, concentration and focus on Wolfsburg from all players. We didn't have that feeling with Max. That's why he's not there," Kovac told German broadcaster Sky Sport.
Kovac, the former Bayern Munich and Monaco head coach, added: "We didn't see any impetus from Max that he could help the team. The club is more important than everything else and that's why we made the decision together.
"We informed him that he will not play a role for us in the future. No more games."
Schafer added: "He will never play for VfL Wolfsburg again."
Kruse signed an 18-month deal when he joined Wolfsburg in January, meaning he faces playing no games until next season unless he finds a new club in January.
He won 14 caps for Germany from 2013 to 2015 before falling out of favour, while he also played three games for the Germany Olympic team at Tokyo 2020.
Earlier this season, Kruse had questioned his level of involvement at Wolfsburg, with his first three appearances coming off the bench.
He then started against RB Leipzig and Koln, but in 270 minutes of action in the 2022-23 Bundesliga he failed to register a goal or an assist, and managed only two shots on target, before Wolfsburg pulled the plug on his season.
