The Gers, who had previously recorded draws at Peterhead, Berwick Rangers and Annan Athletic as well as losing at Stirling Albion, overcame Clyde yesterday afternoon thanks to goals from Dean Shiels and Lee McCulloch.
"There was a lot of pressure put on us by the media," said Hegarty. "It's definitely a big positive for all the lads getting our first away win.
"When we don't perform, the lads get annoyed because they want to do well for themselves.
"We just had to go out there and put on a really good performance. I think we showed that."
Rangers currently top the table, having taken 18 points from nine games.