The Hammers are currently 12th in the table with seven games left to play but Collins believes that they have enough talent in their ranks to initiate a last-minute push into the top half of the table.
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|3/1||West Ham are 3/1 to finish in the top 10 of the Premier League with BetVictor
"If we can go to Southampton and get all three points on Saturday, then tenth place will be on."
Collins put in an impressive defensive display at Anfield and admitted that the game was a difficult one.
"It was tough. They are so sharp and quick on the ball," he admitted. "You have to be on your toes for 90 minutes and it was probably one of my best games.
"Anfield is a tough place to go and although we've had some good clean sheets on the road this season, West Ham's record there over the years hasn't been great."
West Ham almost stole victory on the stroke of full-time, but Jack Collison's headed effort was cleared off the line by Lucas with just four minutes left to play but the defender says he is happy with a point.
"We could have even won the game from a corner near the end," he continued.
"Set-plays are a massive part of our game and we do a lot of work on them, in defence and attack.
"We knew that would probably be our best chance and Jack has got his head to one which was cleared off the line.
"Looking back though, we will take a point with the amount of possession that they had."
Meanwhile, manager Sam Allardyce is aiming for one more win this season, believing three more points will guarantee safety and another year of Premier League football.
"I'd like another three points," he told reporters. "It depends on teams below us because some are picking up two or three wins back to back but we are looking up, not down."