Hazard netted his first Premier League goal of the season in the 51st minute to give Chelsea a deserved win at the Vitality Stadium, ensuring they remain nine points behind rampant leaders Manchester City after 10 matches.

City have won 13 of 15 games in all competitions this season, scoring 45 goals, while Chelsea have already tasted defeat three times in a campaign hindered by injuries to Hazard, N'Golo Kante and Alvaro Morata.

"At this moment we must be realistic by going game by game," Conte said when asked if Chelsea are aiming for a top-four finish rather than retaining their title.

"We have 19 points and we deserve to have 19 points. We are first in our group in the Champions League. We went into the next round of the Carabao Cup after going out in the second round last season.

"This group [of players]... I'm very happy for this group. There are players who are very honest, players who want to fight until the end for something important. Are we able to do this? I don't know. But we will try to stay there.

"I know very well that in England, in this league, there are six top teams. Four go into the Champions League. Two have to stay out and play Europa League. Last season we saw this. It was very, very, very difficult."

Chelsea kept just their fifth clean sheet of the season and their margin of victory might have been greater if Morata had converted two good opportunities to break the deadlock in the first half.

"For a big part of the game we played very well, with maturity and good possession, and tried to create and find the right ball between the lines, or to switch the plan," Conte added. "We created many chances to score. We could have been more clinical in the first half.

"In this type of game, you must be able to kill the game. If you keep the result in the balance, you risk drawing in the end. But I think we deserved to win.

"A good win for our confidence, a good win before another tough game against Roma in the Champions League. I think I saw a lot of positive things."

On the subject of Morata's performance, he said: "Honestly, I'm happy with his commitment, his desire, his will to fight. For sure, he can do better but, don't forget, he is recovering from a muscular problem.

"When you have this type of problem, it needs a bit of time to come back to the best physical condition. I'm very happy with his performance."

After the match, both Hazard and Cesar Azpilicueta admitted Chelsea should have killed Bournemouth off more comfortably than they did.

The Belgium forward, who has now scored five goals in his last four meetings with the Cherries, said: "I like to play against them. I try to play every game like this -- against them, against everyone.

"I scored the goal, we won the game so I'm just happy tonight.

"The only problem today is we should score more goals, in the first half we could score three or four.

"It's not easy to control the game when you are just 1-0 up, but defensively we were strong, we did not concede many chances.''

The lack of any extra goals left Azpilicueta and his defensive colleagues to see the game out in the face of a late Bournemouth rally.

And the Spain international said: "I think we controlled the game, we could score more goals.

"At the end they pushed but we defended well and got away with the three points.''

With Manchester City's imperious form, there is little room for error in the Premier League title race.

And Azpilicueta said: "We have lost already three games and there is no room for mistakes now, we have to keep winning.''

Chelsea's focus now turns to Tuesday's away clash with Roma in the Champions League, and Conte hopes to have Kante available for selection after three weeks on the sidelines with a hamstring injury.

"He could be ready," Conte said of Kante. "You know very well the importance of this player. I want to be sure he is ready. Honestly, I hope to have him in this game. But I'd prefer not to take a risk. If he's ready, he plays."