The Belgian centre-back was sent off after only 10 minutes of City's 2-0 victory at Hull, meaning he will not captain Manuel Pellegrini's men against struggling Fulham next week.
Dzeko, who hit a late goal to rubber-stamp the points after David Silva had opened the scoring, praised his team-mates for staying strong without their influential skipper.
The Bosnian told BT Sport: "Vinny is our captain and our leader, our heart, and I hope he will be back soon so we can win games together.
"We showed character with the 10 men over 80 minutes and we did a good job.
"We were fighting all game because we knew what the game meant for us. We won the game and that's important.
"The next game against Fulham is important and we will try to win that."
It was a bad-tempered encounter at the KC Stadium as an early flashpoint saw Kompany shown a red card for his professional foul on Hull striker Nikica Jelavic.
Only four minutes later, Silva scored a wonderful curling goal.
After the break, substitute George Boyd and the incensed City keeper Joe Hart clashed when the Hull forward tumbled in the visiting box and appealed for a penalty.
But Dzeko made sure of the victory that lifts City to within six points of leaders Chelsea - who play Aston Villa on Saturday evening - with a late goal on the counter-attack.
City boss Pellegrini hailed the win as a "professional response" to back-to-back defeats to Wigan and Barcelona, results which saw the Manchester club exit both the FA Cup and Champions League in quick succession.
"We needed to win today and playing with one player less for 80 minutes is very difficult, but I think we did a very good performance," he said.
"We defended well with and without the ball but we also attacked a lot. It was a very professional response from the players."
Referring to Kompany's dismissal, he added: "It was clearly a foul from Jelavic but the referee didn't see it or didn't give a foul, so after Kompany's foul, he is the last man and it's a red card, but there was a foul before that.
"But I just want to talk about my team, we had a very good response in a difficult week."
Although Hart appeared to be the aggressor in the second-half flare up involving Boyd, Hull manager Steve Bruce was more concerned with possible simulation from his own player.
"I will have a word with George about when he's gone round (Hart)," Bruce said. "In that situation players are waiting for it and when you're at full tilt, you should be waiting to get out of the way.
"I'll have a word with George on Monday and see what his thoughts are."
The defeat leaves Hull only five points clear of the relegation zone and Bruce admitted feeling some frustration about his side's failure to force the draw.
He added: "I think the turning point was the goal Silva got. Had we gone 15 or 20 minutes without them scoring then it might have been a different situation.
"We were continually chasing the game and when you do that against a quality side who are defending deep with 10 men then you huff and puff and get frustrated. It was a difficult afternoon."