He also said the West Ham board deserved credit for spending the money on bringing him in.
Haller, 25, moved from Eintracht Frankfurt for a fee that could total £45m after scoring 51 goals in 98 games for the German side.
Talking on the Alan Brazil Show (talkSPORT, Wednesday, 9.30am), Cottee said, “First and foremost West Ham paid a lot of money, an incredible amount of money for him. Credit to the board for spending the money.
“However, that puts pressure on a player, he’s the £45m man and he’ll be judged on goals. If you play rubbish but score the winning goal you’ll get the praise.
“What I like about him, right from the first 20 minutes against Man City, he was putting it about, and he’s now got his goals.
“The best was his finish against Watford from three yards out. It’s an art. You’re getting in the position, there’s no one near you, it’s because you’ve got a football brain to get in that position. Everyone was raving about the overhead kick but I was interested in the tap-in.
“If you can get 15 tap-ins a season, that’s your goals. No one’s done it for many, many years for West Ham. It’s early days for Haller, but I think he can do it.”
Goals an issue for West Ham
Cottee is bang on when he says goals have been a problem for West Ham, and their record in the Premier League is awful.
The last time any West Ham player scored over 15 goals was back in the 2004/05 season when they were in the Championship.
That season Teddy Sheringham scored 18 and Marlon Harewood got 17.
Since then it’s been a struggle getting into double figures in the league.
Marko Arnautovic scored 11 in the past two seasons, Michail Antonio was the top scorer in the 16/17 season with nine, Dimitri Payet got nine the season before that.
West Ham have paid top dollar now and they’ll be looking for 15+ goals from Haller and he’s already on his way with three. If he can reach Sheringham’s tally from 04/05 they’ll think it’s been money well spent.
TiF Tactics – What does Haller bring?
According to stats site WyScout, Haller boasted an xG of 0.47 across all competitions last season and scored 0.52 per 90. He also added an assist every 360 minutes and won half of his 13 aerial duels.
As Cottee pointed out, he’s got a striker’s brain and can score with his head and from close range, as well as contributing with the odd acrobatic effort.
According to WhoScored, from his 0.5 goals per game last season, he scored 0.4 with his right foot, 0.1 with his left foot and 0.1 with his head. That’s a striker who can score all sorts of goals.