The latest defeat inflicted by Crewe has left the Gills outside the relegation zone on goal difference.
Hessenthaler said he received a text from chairman Paul Scally after the 3-1 defeat saying: "Keep the boys confidence up - great effort."
Hessenthaler told BBC Radio Kent: "To get a message like that shows he's right behind me.
"I'm here to do a job. I signed a three-year deal and I'll see those three years out."
Meanwhile, Hessenthaler gave his vote of confidence to teenage debutant Callum Davies, after the 17-year-old was sent off just 28 minutes into his first appearance.
Hessenthaler added: "He said sorry to me, but he shouldn't. He's done nothing wrong."
Source: PA
Source: PA