Second placed Rose prevailed 2-0 at Broxburn last Thursday to move onto 50 points from 21 games, within a point of leaders Penicuik Athletic who have played one game fewer.
"The boys have got a target on their backs with this run,” Herd told the Journal and Gazette.
"People are determined to stop it so every game’s got an extra incentive for the opposition.”
Although Rose appeared to win comfortably enough at Broxburn – thanks to a fine Alan Docherty strike and Mark Stowe’s late penalty – Herd stressed it was not all plain sailing.
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Average league attendances for all 42 SPFL clubs in 2019/20 season
"It was a good game for us after the first 20 minutes or half an hour,” Herd said.
"Broxburn made it a wee bit uncomfortable for us. They kind of just sat in and stopped us from playing and we didn’t look like ourselves.
"So we had a wee word with them at half-time and they came out and responded. In the second half they were excellent.
"So it was a good night’s work at a venue that’s been quite tricky for Linlithgow over the years."
On being just a point behind Penicuik, Herd added: “We knew coming into the festive period that if we could come away with maximum points we would be right on their tails.
"I’ve had the boys tuned in from November, December how big the festive period is.
"So it’s a big well done to the boys.”
Rose will start as massive favourites to win this Saturday’s home league game against lowly Blackburn United.
But their gaffer, a former boss of Camelon Juniors, is taking nothing for granted ahead of the Prestonfield encounter.
"In this league if you don’t play well and you’re not at it you’ll get found out,” Herd said.
"It’s just up to the boys to carry on the mentality, the work-rate and Saturday will take care of itself.
"But we need to be wary of Blackburn, they’re fighting for their lives so they come and give it everything to try and get a point or three points.”