Sarri admitted his side suffered a "horrible" 15 minutes which could have cost them dear.
Emery said: "It is clear the result is not good for us but the process is continuing".
"We dominated the first 30 minutes and created a lot of chances, but in the Premier League if you drop your level it can let in the other team", Pochettino said.
Chelsea looked on course for an easy win over their London rivals after Pedro and Alvaro Morata put them 2-0 up after just 20 minutes at Stamford Bridge.
Bournemouth took full advantage of comic home defending to strike twice in six second-half minutes through Callum Wilson and Steve Cook, inflicting Manuel Pellegrini's second successive defeat since returning to the Premier League with West Ham.
New managers Maurizio Sarri and Unai Emery will have their first competitive impressions of the match on Saturday after having already met in a 1-1 pre-season draw, which Arsenal won 6-5 on penalties.
Lyric McHenry dead: EJNYC star dies aged 26 at 20 weeks pregnant
According to published reports , McHenry once worked on a reality show about fashion and social issues on the E! cable network. The reality star reportedly died from a drug overdose, however her cause of death is still under investigation.
On Emery's half-time team talk he said: "We were on a high". I think we have to work and we have to improve.
Sarri turned to Hazard and Mateo Kovacic in the second half and the Belgian forward's run and pass led to Marcos Alonso's victor.
"It was a hard game". A very important three points for us'.
Oliseh who laid initial foundation for Nigeria's qualification for the recently ended 2018 World cup in Russian Federation took to social media to express his delight over Iwobi's performance especially in the first 45 minutes of the battle of Stamford Bridge Saturday.
'We have a squad of 23 players and everyone in the squad needs to be ready to show the manager that they deserve a spot.
The former Sevilla coach has yet to win a game after two losses, following their defeat to Manchester City last week. We didn't score, they managed to and we lost.
Unai Emery will without a doubt drill his midfielders into stopping the ball from being played, as well as the defenders for sticking tight to the runner.
Everton's revolution under Marco Silva gained more momentum at Goodison with Richarlison scoring his third goal in two games.