Before the Blues kicked off on the south coast, Tottenham Hotspur beat Watford 4-0 to move to within four points of leaders Chelsea.
But Conte's side were were seldom in danger as they restored their seven-point advantage.
But man-of-the-match Marcos Alonso made the game safe with an exquisite free-kick and Conte said: "Yes, I'm satisfied because it wasn't easy to play this game after the win by Tottenham but our answer was very good.
"We started very well with a will to win the game," the Italian added.
"It was a pity to concede the goal and we suffered a bit but in the second half I think we managed the game very well and scored a second to improve the result against a really good team, with good organisation and a good coach. We must be pleased with the game.
"It's not easy to play after Tottenham but I think it's normal in football. When you play after your opponent it's normal if you see that the opponent is very close to you to feel a bit of pressure.
"But I'm happy to face this kind of situation, to play with only four points' advantage. I like the pressure, to live with pressure. If I don't see pressure, I put some on. When you have pressure, you give the best of yourself. We accept it.â
- 'Don't smell victory' -
Conte, however, would not accept that two victories in quick succession after last weekend's surprising defeat by Crystal Palace had guaranteed the title for Chelsea.
"I don't smell victory yet because there are seven games to go, we have a schedule that's not easy and we know this,â the Italian said.
"It's important to go game by game. After losing to Crystal Palace, we played City and could have dropped points and today we could have dropped points. Instead we won both games. We have to go on in this way, game by game and stay concentrated.
"For sure Tottenham have a great desire to win the title and we must have the same desire. Don't forget that last season they played for the title and we were tenth, so they are a really good team.
"I think Tottenham are stronger than last season, they reinforced their team with really good players. It's important to understand this.â
However, Conte did agree that the battle for the title was now a two-horse race involving his side and London rivals Spurs.
âIt's just us,â he said. âI don't know the other teams' results but I think there is a space between us and the other teams. I don't think there is space for them.
"It's logical that if we and Tottenham continue to win, it will be a race between us."
Diego Costa has now gone five Chelsea matches without a goal but it was his shot that Smith deflected in and he went close twice more.
"I'm happy with his performance," Conte said. "In this moment Diego is not scoring but he's totally involved in the team and he continues to work with commitment and desire. He provoked the first goal and I'm sure he can score in every game."
Bournemouth manager Eddie Howe accepted the better team had won.
"They are hard to play against," he said. "At Stamford Bridge we tried to play their way and lost 3-0. Today we played our way and that didn't work either.â