"Every game is vital now but if we can go unbeaten to the end of the season and win some we won't be far away," he says.
"We need to make four points up but I think that is feasible. All I know is we are playing a lot better, with a lot of spirit.
"Fredi came on on Saturday and showed that he is eager to play and that he is fit and strong - which all bodes well for the last six games."
Paul is hopeful that Steve Lomas can return to action against Aston Villa after pulling up at half time against Southampton at the weekend and he explains: "In the international break Steve had to play two very tough games - one in a side with only nine men - so he obviously had to do a lot of running.
"He just felt his thigh go tight, but thankfully he didn't pull anything. It was an incredibly hot day, we had to do a lot of chasing, and that saps your energy."
He admits that the team, and the man of the moment Jermain Defoe didn't perform at 100%, but is delighted with the way he took his goal and the resilience the side as a whole showed at St Mary's.
"Jermain had had a poor game," says Paul, "and couldn't get hold of the ball.
"We starved him a little bit of good service - but he is a goalscorer, and he came to life a bit after getting the goal.
"Credit to Southampton as well, they played some good football and were very competitive, making it a tough game.
"We weren't awful, we just didn't reach the heights that we think we can.
"If people had said you were going to get a point at Southampton you would have taken it because it is a tough place to come - it was a good result for us."
Of the fracas on the bench which saw a member of the Southampton coaching staff encroach on West Ham's technical area as Glenn Roeder held Chris Marsden as he was having a tussle with Lee Bowyer - for which they both got booked - Paul dismisses any bad feeling.
"Dennis Rofe came flying across but it was fine, there was no problem," he says.
As for the battle ahead, he concludes: "There are a lot of people in it; it is going to be tight and we have to concentrate on every game we have to get results."