The Saints came out on the wrong end of a 2-1 scoreline at St Mary’s, despite having pulled 1-0 ahead during the game.
At the final whistle of the Premier League encounter boos rang out amongst the crowd and many feel Hasenhuttl is under pressure.
Southampton have lost four of their last five Premier League games, but Hasenhuttl does not believe his side were too far off against Everton, with just a lack of ruthlessness telling.
“Premier League football is good and when you don’t score you concede, it is not enough to invest a lot and create. You have to be decisive”, Hasenhuttl was quoted as saying by the Daily Echo.
Asked if he is under pressure, the Southampton boss hailed the fans, while stressing that the team will come good.
“I must say the crowd was fantastic during the 90 minutes and this is what we need.
“The team will be a good team but they need time”, he added.
Southampton could struggle to return to winning ways next time out with a trip to play champions Manchester City on the agenda for next weekend.
The next visitors to St Mary’s are David Moyes’ fellow strugglers West Ham United.