Eddie Howe's players pointed out that Salah had been in an offside position but their complaints were dismissed, although TV replays suggested they had a case.
The Egyptian became the fastest player to 40 goals for Liverpool in the Premier League as he ran rings around the Cherries.
Speaking of Milner, Salah said: "I want to congratulate him on his unbelievable career, he deserves it".
The win put Liverpool atop the Premier League standings, one point ahead of Manchester City.
'It's a big blow, especially with the form he's been in this season, his athleticism, pace and strength is always a real weapon for us. "We were very controlled in the first half, scored the goal but I wasn't completely happy with the rhythm changes".
Salah also turned down the Man of the Match award at the end of the game to give it to Milner who was making his 500th Premier League cap.
Beaten by Wolves last time out, Chelsea were a different team altogether and from their first corner, on 78 minutes, Luiz headed home the second goal.
"So far we showed consistency, which is the most important thing". It was not the most impressive finish but I would say it was pretty surprising [for the goalkeeper].
"Whatever you do in a football game you have to finish off, and what Mo did was exceptional". Unfortunately I can not say it will never happen again, but we are really more controlled in these situations and that was a big step for us, very important.
Bournemouth hosts Liverpool in a Premier League fixture on Saturday, Dec. 8.
"I do think the only way to be successful is to be completely focused on yourself, that's what we try to do".
On the other hand, Milner has hailed Mohamed Salah as "unbelievable", and revealed his delight at reaching the 500-game milestone.
On Salah's determination to stay on his feet when he could have gone down under a challenge by Cook before scoring his second...
The result was in no question when the brilliant Robertson's cross towards Mane's direction was met unwittingly by Cook, who saw the ball enter the back of the net past his own keeper.