Villa have won only four home games this season and are five points above the drop zone after Saturday's goalless affair with Sunderland - their 15th draw of the campaign.
Given said: "It has been frustrating the whole season. We haven't had enough victories at home. We don't want to stumble the wrong side of the line because we know we are not safe yet. We are five points clear but Wigan have shown any results can happen at the bottom."
He added: "The thing for Aston Villa is we can't rely on other people. We have to do the job ourselves.
"Ideally we want to win against Bolton but it is easy enough saying we want to win. We have to go out on the pitch and do the business."
Given, who made the ?5million move from Manchester City last summer, believes Villa have under-achieved.
He said: "We don't want to be where we are at. But we are where we are and there is no getting away from that.
"The table never lies and we are where we are because we deserve to be there. We don't deserve to be any higher as we haven't picked the points up.
"I don't think it was always going to be a difficult season. I think we have under-achieved as a club and as a team.
"We've had injuries and the young lads are coming in with big pressure on their shoulders and it is tough on them as well."
Source: PA
Source: PA