Patrick van Aanholt’s equaliser, scored from an offside position, had drawn Palace level until the 87th minute, when Sakho’s reckless action left referee Mike Dean with no option but to award a penalty, while the defender was perhaps fortunate to only receive a booking.
The hosts’ substitute Junior Stanislas capitalised by scoring his first Premier League goal since his return from a six-month absence with a knee injury, consigning Palace to a fourth defeat from seven.
Hodgson said: “The ball is hit into a crowded area and the referee blew his whistle. We didn’t have a clue what had happened at the time.
“Mamadou Sakho has no intention to elbow the player or use an elbow to stop the player getting to the ball.
“I can’t deny that, when you see it on the television, he does catch the player and as a result the referee is quite within his rights to give the penalty.
“It’s always frustrating losing to a needless free-kick given away (by Alexander Sorloth, just before the penalty), and then to a penalty.
“Especially after doing so well, first of all, to get over the shock start and wonder goal (David) Brooks scored, and then get ourselves on to an even keel and on the front foot in the second half, showing a lot of initiative.
“We paid a high price for the mistakes we made. We end up with nothing to show for our efforts.
“(Sakho) feels aggrieved. We are used, in football, when you give a penalty away it’s because you’ve deliberately stopped a player scoring a goal. But not with an unintentional collision.”
The victory takes Bournemouth up to seventh — six places above Palace — and their manager Eddie Howe hailed the impact Stanislas made only three minutes after coming on as a substitute
Howe said: “I’m really pleased. It was a very tough moment for him.
“He’d not touched the ball. He is the penalty taker and grabbed the ball. But it’s not easy to get the composure to grab the ball and take it. It was a huge moment for the team.
“It’s been a long journey back from injury for him. We are delighted Junior was on the pitch as he has such a cool head.
“We had to defend well. We shaded it and deserved to win. They did well for long spells in the second half. But I was pleased with the mentality of the group to go again after conceding the equaliser.”
Brooks’ outstanding finish had given them the lead in only the fifth minute and represented his first goal for the club following his £10million transfer from Sheffield United.
Howe added: “He has outstanding technical qualities. He’s a goalscorer in waiting. (It was) a big moment for him.
“He’s started really well in his time with us, and the potential of his performances are huge.”