While supportive of Potter's appointment, Cottee concedes the "club is a mess" and the team needs major surgery after a first-half of the season which saw Julen Lopetegui sacked.
He told Tribalfootball.com: "Potter has done a good job at Swansea and Brighton before his spell at Chelsea which was always going to be a difficult role for him. If you've got talent, you don't lose it. He may have been away from football for a year or two but his talent is still there and he is a young manager who was waiting for the right opportunity.
“The club is a mess at the moment and taking over from the Lopetegui era was never going to be an easy task for anyone but it was a promising performance. Graham has to get a few of his own players through the door in January and start to prepare for next season rather than worrying too much about this season.”
On the downfall of Lopetegui, former striker Cottee says he wasn't surprised.
He continued: “Honestly, I didn't think Julen Lopetegui was the right appointment in the first place. I think there were three or four other managers that should have got the job ahead of him, he was right down the list for me. Graham Potter was one of those managers that I thought offered more and would have been a far better appointment.
“I don't like saying ‘I told you so’ but I did tell everyone. I just couldn't understand why the club went down that route with Lopetegui, I didn't see what he brought to the table. The club should have gone in a different direction and sadly they chose the wrong option. It has cost them a lot of money to fix their mistake when they could have appointed Potter originally.”
Meanwhile, West Ham appear short of quality upfront with Michail Antonio and Jarrod Bowen both sidelined. However, Cottee says the squad has enough attacking talent to handle their absence.
"His (Potter's) aim should be to get more out of West Ham’s flair players such as Lucas Paqueta and Mohammed Kudus who have been inconsistent this season," said Cottee.
“West Ham have got to be stronger at the back. They have been conceding far too many goals this season and they shipped another two on Friday. A highlight was watching young Ollie Scarles play left back, he's a young kid who played in our youth team and won the FA Youth Cup. As a West Ham fan, we all want to see our academy players given a chance in the first team and despite being substituted he played exceptionally well for 70 minutes. I was so pleased for the young lad.”
Cottee added, “But West Ham do need a well-rounded striker who can lead the line, hold the ball up, and bring other players into play which isn’t easy to find in January, especially on a budget. We have four centre-forwards at the club, three of them are injured and the other one is Danny Ings who isn’t fit enough to start lots of games during a busy schedule. We need someone to come in who can lead the line for the rest of the season and score goals in the Premier League."
- Tony Cottee was speaking to Tribalfootball.com on behalf of BetUK