Spurs won 5-1 against the south coast club in their latest fixture, as Kane got his season up and running.
The 22-year-old had struggled for goals over the opening weeks of the season, but he now has four strikes to his name and Eriksen believes the striker will be able to kick-on.
"Harry has been under pressure from everyone else as well as himself but that comes when you’re used to scoring in the Premier League," he said.
"As a striker you have to be in the right place at the right time and he was there.
"Now he’s scored but we all know what he’s capable of."
Eriksen’s words were backed up by Eric Dier, who also stated that he never had any doubts over Kane’s ability to score.
Even though the England international hit the back of the net just once in 13 games, Dier claims it was only a matter of time before he rediscovered his spark.
"He kept working, kept doing the same things he did before, we all knew the goals would start coming and that’s what has happened," the defender said.
"Everyone is delighted for him and hopefully he'll now kick on and score many more.
"Harry keeps working the same way every week for the team and that's important."
The hat-trick against Bournemouth allows Kane to play with a lot less scrutiny on him from outside sources, and the hope is that release of pressure will see him get back to his best.
Tottenham’s next match comes against Aston Villa on Monday evening, and they will be aiming to take their unbeaten Premier League run into double figures.