Hessenthaler told BBC Radio Kent: "We knew it was coming. We've been hurting for the last couple of weeks as we've had a lot of criticism.
"We've shown strong character but it's only one win. We've got to now go and take that onto Barnet on Tuesday."
The trip to meet the Bees will see Gillingham face Hessenthaler's predecessor Mark Stimson, who left Priestfiled in May and took over at Underhill in June.
"It'll be a good atmosphere," said Hessenthaler. "We know a lot about their players and obviously Mark knows a lot about our players so it will be an interesting evening.
Finally, we get an away win
Seymour Totti
"Obviously it's spiced up because Mark was manager here so I'm looking forward to it, but it's just a game of football."
Gillingham's poor run of form away from home began under Stimson, with the Gills unable to win on their travels last season on the way to relegation from League One.
That run continued under Hessenthaler, with Gillingham needing a further 10 games this term to break their away-day jinx.
"It's great to get rid of that now and we've got to look forward to the next game," added Hessenthaler.
"But I don't think we can look any further than that. Our most important game is on Tuesday."
Source: BBC Sport
Source: BBC Sport