Darren Way has urged supporters to stick with the squad as they prepare for final 11 matches of the 2016/17 Sky Bet League Two campaign.
The Glovers have been on a difficult run since the turn of the year, winning just one of their 12 league games (D7 L4).
Saturday’s defeat to promotion-chasing Luton Town means Town are eight points above the relegation zone following Leyton Orient’s win at fellow strugglers Newport County.
Yeovil were bottom of the table when Way took over on New Year’s Eve 2015 and the 37-year-old led the club to safety with four games to spare.
Way’s side are five points and three places better off than they were at this stage last season, and says he will do everything possible to make sure Town are in the EFL next year.
He told YTFC.net: “We are where we are as a football club and if I was a supporter I would be frustrated and they’ve spent three years like that.
“They feel that the club is turning round, then feel like it’s going back again - I can understand their disappointment.
“If I could ask us all to stick together and do everything we can to stay in the football league because I knew how that difficult that was last year and I knew this year as manager was going to be my toughest test.”
Way continued: “I’ve been in a very difficult position over the last three years as a coach and manager where we’ve been losing constantly. I don’t want to go back to that habit and I want good performances.
“I have to manage this from now until the end of the season and I have to do it well.
“As a manager sometimes you have to stand there and take responsibility, something I’m not afraid of.
“I will take responsibility and the criticism. I’ll do everything I can to protect my players as they are still giving everything.
“A top manager told me this week ‘in this job you can run, but you can’t hide’ and one thing I’m not going to do is hide.”