The Bees' recent dip in form, when they failed to win in seven matches until beating Port Vale last weekend, resulted in murmurs of discontent from sections of the crowd.
Kleanthous said: "There is no-one who understands how important winning is to our fans more than me. Their passion is one of the reasons I love this club.
"However, we need to use that passion to good effect and start backing the team as soon as they cross the white line on matchdays.
"Of the 11 games remaining until the end of the season, seven of them are home matches, so you have a very big part to play in how we finish the season.
"The club, management, Lawrie Sanchez, the players and the supporters must all be 100 per cent together."
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