The Saints beat National League South leaders Welling United 2-0 on Tuesday night.
It was hailed by fans as the club’s finest performance of the season so far.
Allinson was quick to praise his players, who have now taken 15 points from their previous six matches.
While the manager stopped short of calling it their best yet, he knew it sent out a message to the rest of the league.
The Saints jump to fifth and this weekend face a tricky trip to Dulwich Hamlet.
“I think it was an excellent performance from back to front,” he said. “I’m really proud of the players.
“There are a lot of good sides in the league this year and Welling are certainly one of them.
“But it’s a very demanding season and we’re going to keep our feet firmly on the ground, it’s the only thing we can do.
“You can’t afford to get carried away but the results in the league right now are very encouraging.”