The Trotters managed a point against Swansea at the Reebok Stadium on Saturday but QPR's victory over Tottenham left Owen Coyle's side four points adrift of safety.
Bolton's hopes of getting out of trouble rest largely on the fact they have 15 points to play for while most of their rivals only have three games left.
Their next opportunity to close the gap comes at Villa Park in two days' time in a match postponed from last month following the cardiac arrest suffered by Bolton midfielder Fabrice Muamba.
Right-back Steinsson conceded Wanderers' plight is having an effect but he remains confident they can secure the points they need.
He told Press Association Sport: "There's a lot of pressure because if you concede goals the plan is gone but playing against a team like Swansea that keep the ball really well it's important to accept that maybe a point is good enough and start focusing on Tuesday, because that will be a big game for us and a big game for Villa. It's important we make the most of our games in hand.
"We need to get points out of every game we've got left and wait and see the result. It's in our own hands, if we do our job and get the points we need, we will stay up.
"If we fail to do so the disaster will happen, but we've got all the confidence in each other and I know we'll go on and get out of trouble."
Coyle had targeted three points from Saturday's game but in the end they were grateful for one after surviving a barrage of Swansea attacks, particularly in the second half.
Both goals came early in the game, with Scott Sinclair getting the better of Steinsson in the sixth minute before planting a superb shot into the top corner, while Martin Petrov set up Chris Eagles for the equaliser eight minutes later.
Steinsson was a key figure in Bolton's defensive effort, blocking goal-bound shots on a number of occasions and also nicking the ball off Sinclair's toe when he seemed certain to net his second late on.
"We defended really well, we blocked a lot of shots," said the Icelander. "We couldn't really get the clear-cut chances we were after. We took a lot of chances, we tried to press them high up. It was high intensity, high tempo.
"The last line of defence needs to put your body on the line. It's a great cause and we'll do that at every opportunity if needed. Tim (Ream), David (Wheater) and Sam (Ricketts) as well, we did our job. Unfortunately we conceded a goal early in the game but we got one back quickly."
After four defeats in a row, Swansea made it four points from their last two games following victory over Blackburn.
Boss Brendan Rodgers praised the attitude of his players and commended Bolton for their fighting spirit.
"The consistency of our performance level right the way through the season, up until a few weeks back, has been fantastic," said Rodgers.
"We had a little blip in terms of results and the performance against QPR but I think the reaction since then shows the mentality and the improvement among the players.
"Bolton's a brilliant club, they've obviously gone through a lot, especially in the last couple of months, and maybe another team might have folded with the pressure we were putting them under, especially second half. So you've got to give credit to them and how they're still fighting."