Michael Leary fired the visitors into a fourth-minute lead, but Lewis Chalmers equalised soon after half-time and the Shots laid siege on Cole's goal. But he produced excellent saves to deny Anthony Straker and Kirk Hudson.
Cole was signed on loan from QPR last month and his arrival has coincided with Barnet's five-game unbeaten streak, leaving Hendon determined to tie his new number one to the club.
Hendon said: "I've spoken with QPR. It's all up in the air with their manager situation and I want to keep him here even if it's just for three games.
"But I've made the phone call and I want to keep him at the club for as long as possible. If you look at his performance you can see how important he has been for us in recent matches.
"It was probably a fair result. It wasn't pretty, but it was a well-fought game. I'm disappointed because I thought the game was there for the taking and I want to win games like that, but the lads were dead on their feet so maybe I'm being a bit harsh."