West Ham drew 1-1 with Crystal Palace on Saturday afternoon as Wilfried Zaha finally cancelled out Mark Noble's first-half penalty. Palace had a number of excellent chances to win, but failed to do so.
The Hammers have gone five matches in all competitions without securing a win, though they did earn a point against Liverpool last Monday thanks to Michail Antonio's goal.
Former Hammers striker Harewood reckons the club are good enough to finish in the five of the Premier League with the squad of players they have, despite the east Londoners sitting 17 points behind sixth.
"It's one of the those things. We have got some top class players, no doubt that that," Harewood said. "If you look at West Ham, they're a top five, top six team, that's my opinion.
"The players they've got there - especially with the performance against Liverpool - they should be in the top five. Top five is my opinion, if they play like that against Liverpool, then they can get top five."
West Ham have produced some marvellous results, beating Manchester United and Arsenal as well as drawing with Chelsea and Liverpool, but it is their results against lesser sides that see them struggle.
The Hammers have a crucial run of games coming up, as they face winnable fixtures against Cardiff, Fulham, Newcastle and Huddersfield in their next five games - also playing Manchester City.
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