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Despite scoring first at the Vitality Stadium on Saturday, the Blues could only manage a 2-2 draw against Bournemouth.
Alonso fired the Blues ahead after half an hour at the Vitality Stadium.
Bournemouth hit back shortly after the break when Jefferson Lerma rose highest to power a header beyond Willy Caballero.
Josh King then tapped home at the back post following good work from Jack Stacey before Alonso pounced to nod home the equaliser after Pedro’s shot was saved.
Chelsea boss Frank Lampard blamed lack of concentration for Chelsea’s failure to get a win at the Vitality Stadium.
“We should win, we had many chances,” said Lampard.
“We had a bad 10-minute spell where they scored and that I don’t like. I’m pleased with the character to get a draw but we should win the game.
“Against Bayern we conceded twice in a short space of time, it’s not the first time. Could it be a lack of concentration? Possibly from the players.”