The Hammers currently sit rock bottom of the Premier League having only managed eight points from 12 games so far this season.
They have thrown away leads to draw their last two games against Birmingham and West Brom, with Ian Holloway's Blackpool set to visit Upton Park on Saturday.
Parker, 30, is troubled by the manner of West Ham's performances, and is desperate for a quick turnaround.
"The whole team needs to be more defensive-minded," he said.
"When we get into a winning position we need to see the game out and we are struggling to do that.
"It's one thing to concede from a 40-yard screamer or when a player beats four defenders and curls one in to the top corner.
"But when an opponent gets a free header three yards from goal - like West Brom's equaliser on Wednesday night - that is just not acceptable.
"We can't keep on allowing sloppy goals like these if we are going to turn draws into wins."
Co-chairman David Sullivan last week demanded a minimum of seven points from the next four games, but West Ham's latest stalemates leave them needing victories over the Seasiders and Liverpool next weekend to achieve that target.
Parker insists that the players are trying their utmost to climb up the table, and believes they are close to finding their form.
"We are trying our hardest to meet the targets the chairman wants. But it is easier said than done," he added.
"We should have won our last two games and it's our own fault that we didn't.
"Now we have a massive game coming up against Blackpool at the weekend and every home game from now on is going to be hugely important.
"It is important to keep believing we can turn the corner and get out of this position.
"We have had some good performances lately and I think we are very close to turning things around. But we have to start winning at Upton Park and move up the table as quickly as possible."