Stags had the best of a game short on chances, but were undone by a John Akinde goal on the break on 57 minutes.
“We played well, it was a polished performance away from home,” said Allen.
“We restricted them to very few chances and the players stuck to their jobs.
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Click HERE to read Stags boss Adam Murray’s thoughts
It was good defending as a team to defend the lead.
“This is the highest position Barnet has had for a long time. We have got attacking players to come off the bench, which is stronger than last season.
“We have got some good young players who were involved with us today and we are moving in the right direction. It is another three points but there is a long long way to go in this season.”
On Akinde he said: “That is what John does best, get into the space between the last defenders and the keeper.”
Allen also believed the Bees should have been given two penalties.
“I suppose I will have to go and get my eyesight sorted out,” he said.
“They were clear penalties. The referee did get a few things wrong today, but I get more things wrong than anyone. I respect the referee’s view of it.”