"You're getting sacked in the morning" and "You don't know what you're doing" were heard as the Saints suffered a seventh defeat in 10 matches.
"I haven't heard them, my English is not so good," he told BBC Radio 5 Live.
"But I can take it. It is no problem for me because I am responsible for the results. I am the manager here."
Despite that gap, they still cannot be totally sure of survival yet. They have played at least one game more than all the sides below them and end their season with tricky-looking games against Liverpool and Leicester.
Hasenhuttl's side made a poor start in west London on Saturday, conceding two goals in the space of 77 first-half seconds from Pontus Jansson and Yoane Wissa.
They briefly rallied but struggled to create many clear-cut chances, with the visiting supporters growing increasingly frustrated, before Kristoffer Ajer put the game beyond doubt with Brentford's third late on.
"This is not a new situation for me. I have had this pressure my whole life since I have been a manager, and you can be sure for as long as I am here I will do everything to make us more successful," added Hasenhuttl, who has been Saints manager since December 2018.
"We had discussions in the last few weeks about a top 10 [finish]. We had opponents there around us and we were not able to win against them, so we are not a top-10 team. We are far away from being a top-10 team at the moment.
"It's a tough time. We have two games left against two strong opponents and we have to show a reaction, that's for sure."
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