Stephen McManus insists that "everybody needs to stick together" as Motherwell bid to avoid being drawn into the relegation places.
Some fans voiced their frustration during last Saturday's defeat to Inverness Caledonian Thistle.
McManus admits the players have felt the tension in the atmosphere towards the end of recent games.
"It's really important that the fans get behind the players," said the former Scotland defender.
Motherwell have conceded costly late goals in their last three games, but McManus says that there is nothing fundamentally wrong with the way the team is playing.
On Saturday, Motherwell face second-bottom Kilmarnock in the Premiership, with the Ayrshire visitors only two points behind, though they have played a game more.
'Still aiming for top six'
"It's going to be both teams wanting to win because they know what's at stake," said McManus.
"We went through it last year with the play-off games.
"They're not enjoyable occasions. They're great for everybody else, but not to be involved in. Just now, we're just outside it but if we can sustain a run of five or six games, we feel as if we can still make the top six.
"All the teams will be thinking the same because it's so tight, but hopefully we can get a couple of last-minute goals instead of the teams against us.
"When teams are winning, everybody's great, they come to the games looking forward to it, but when you lose the games in recent weeks you can feel the tension.
"That's natural, but the fans at this club have been terrific and you need them."
'No loss in spirit'
Mark McGhee agrees with McManus that the late goals are all isolated incidents rather than a pattern.
The manager remains convinced his team is playing as well as it was during the wins over Dundee, Celtic and St Johnstone in December, but concedes that there are aspects that needs to improve.
"It's for different reasons," McGhee said of the late goals.
"The Thistle game was a lapse in concentration by one of the players. On Saturday it was a poor refereeing decision that resulted in us having a man out of position.
"The Dundee one was a farcical penalty decision. What can you do? You just keep going and hope that it stops and we start doing better.
"I really don't think our form has changed, we're not playing any differently than when we were winning games.
"I feel very confident in the group we have, there's no loss in spirit or determination. The performances overall have been not bad at all. We just need to keep going and hope we find that edge.
"We know what we've got to do better ourselves, we're not saying it's all bad luck. We could certainly do with a bit of support from referees, but we have to do some things ourselves better.
"I don't think [the Kilmarnock game] will be decisive because there are a lot of games after it."
McGhee also confirmed that Motherwell had considered a move for former striker Michael Higdon during the transfer window, but the player had already played for two clubs this season and the rules do not allow him to play for a third in this campaign.