Allen walked out on the Bees after just 19 days to take charge of League One strugglers Notts County on a one-year deal.
Barnet, who are fighting desperately to stay in League Two, claim the Magpies only contacted them after they had struck a deal with Allen and are now seeking compensation for his services.
Bees chairman Tony Kleanthous said: "We agreed a deal with him (Allen) until the end of the season and we helped and supported him throughout.
"I told him that we were prepared to offer a new long-term deal that would certainly have provided him with a comfortable six-figure living but he made it clear that he wanted a chance to manage a team in League One next season.
"He said he wanted to take this opportunity despite the perfect happy working environment which we provided for him at Barnet FC."
Source: PA
Source: PA