Rashford notched his 100th goal for United with a brilliant first-half header, which extended his side’s unbeaten run in all competitions to eight matches.
The rejuvenated striker is the first United player since Wayne Rooney in 2009 to reach the goalscoring landmark and when asked if he could become an elite player, Ten Hag said: “I think he is already.
“Before you’re 25, to score 100 goals, I think you’re already there, but he won’t be satisfied with that.
“In the end it’s about how many trophies you win with your club and I think he can develop his game even more.”
Rashford rose above West Ham’s Thilo Kehrer to meet Christian Eriksen’s cross without breaking stride to give United a half-time lead, which they protected after coming under sustained pressure in the second period.
Ten Hag was clearly delighted Rashford had heeded his advice when the Dutchman first arrived at Old Trafford.
“When you see he made two headers (in the game) for instance and we have worked a lot on that,” Ten Hag added.
“I notified him from the start, his heading had to improve and he worked on that and you can see what’s happening.
“Also mentally, he’s much more consistent and reliable and resilient. I’m really happy with the progress.
“For me he’s already massive, a great player, but there’s still a lot of room for improvement and where it ends I don’t know, but it will be a fantastic career I’m sure.”
Ten Hag also singled out David De Gea and Diogo Dalot after his side climbed back up to fifth place in the Premier League table, one point off the top four.
Goalkeeper De Gea made a string of fine saves, notably from Michail Antonio’s 25-yard screamer and Kurt Zouma’s header.
“It’s quite clear, and I’ve emphasised it several times, I’m really happy with David. He’s a great goalkeeper, he’s only 31 and he’s fit.
“He can progress even more. He was already impressively good for Man United and he will be in the future as well.”
Hammers boss David Moyes, sacked by United in 2014 and yet to beat his former club at Old Trafford as a manager, felt De Gea was responsible for denying his side a point.
He said: “The players put in a good performance, but we’re lacking just the final ingredient, which could make the difference at the moment.
“David de Gea’s two saves were fantastic, they really were. But he’s been a great goalkeeper for Manchester United.
“You don’t be Manchester United’s number one for that length of time if you’re not a fantastic goalkeeper.
“He made two brilliant saves for them and probably saved them from that point of view, but it’s disappointing for us that we didn’t score because we put them under enough pressure.”