The Cumbrians slipped to 19th in the table after losing 2-1 at home to Hereford United on Tuesday.
Former caretaker Abbott was handed an 18-month contract following John Ward's sacking in October 2008.
"I know things aren't perfect at all and there's a lot to do," Allen told BBC Radio Cumbria.
"We've just all got to get behind Greg. We're in a relegation battle and our job is to make sure we don't go down.
"I know there's been a little bit of criticism for ourselves and for Greg but there's no complacency at all. We know we're in a battle and we'll be battling."