Eden Hazard scored to give Chelsea the lead from the spot but the Magpies looked set for a draw after Joselu netted an equalizer during the 83rd minute.
Chelsea got their second goal during the 87th minute after Alonso’s shot deflected off Magpies defender DeAndre Yedlin for an own goal.
Benitez was left unhappy as he believes that neither the penalty nor the free-kick which led to the own goal from Yedlin should have been given.
The win for Chelsea means that the Blues continue their impressive start to life under Maurizio Sarri. They have won all three of their League games thus far under the Italian tactician.
Newcastle meanwhile only have a point to their name and have lost two out of three of the games that they have played.
After the loss against Chelsea, a frustrated Benitez told Sky Sports: “We wanted to stay in the game and try to take our chances. We were very close but the penalty was soft, the foul was soft.
“Maybe they could have scored at the end with the quality they have on the counter-attack but, no, these two situations. It’s a pity because we were very close.
“We knew playing open against them, with their quality and ability, they can beat players in one-versus-one situations. Between the lines, they are very dangerous.
“We needed to be compact, maybe we could frustrate them into mistakes and we’d have chances. The penalty changed everything and we had to be more open.
“We scored a goal but we were so open they had two or three counter-attacks. If they scored from one of these chances, fine, but they had a soft foul and a second ball from a free-kick where we needed to be more aware.”