Erik ten Hag reveals Man United attempted to sign Harry Kane last summer
England captain Kane joined Bayern Munich after leaving boyhood club Tottenham and has scored 43 goals in all competitions for the Bundesliga giants.
Instead of Kane, United recruited Denmark international Hojlund for £72 million from Atalanta - the 21-year-old has so far scored 14 goals.
"We have to win every game," Ten Hag told former United captain Gary Neville on Sky Sports.
"There's an expectation around every game from us so you can only fulfil that expectation when you have those outstanding players."
But the United manager said the Old Trafford club had not always been able to bring in the players they had wanted over the past decade.
"Then you have to build and you have to accept that you get talent in instead of players who have already proved it in the past," he explained. "We have had some choices made with talents like Rasmus Hojlund.
"I can see a striker (Harry Kane) who already proved it, who we want to sign and we couldn't get him. And then we went to Rasmus because he's a talent.
"With Harry Kane you know you get 30 goals. I think Rasmus will get there but he needs time.
"It's not fair to assess him the same as Harry Kane. I would never compare two players because they are very different. But with Rasmus Hojlund, we get the highest potential in the striker position last summer."
United have stumbled badly this season after a positive first campaign under Ten Hag, who has had to deal with a lengthy injury list and a drop-off in form from key players.
They are through to an FA Cup final against Manchester City but were knocked out of Europe before Christmas and have missed out on qualification for next year's Champions League, ramping up pressure on the manager.
However, Ten Hag repeated his belief the club are on the right track, saying patience is needed as young talents progress and players return to fitness.
The Dutchman's future remains uncertain as ambitious new co-owners INEOS look to turn the club around.
Jason Wilcox arrived as technical director recently as part of widespread changes and Ten Hag said there was no time to waste on a rebuild, where he wants to be involved.
"The initial meetings are good, and of course with INEOS several meetings from January on," he said. "Jason first came in last week and now we have to take things quickly because the summer is coming.
"It's a very important period coming when you have another (transfer) window and, of course, we want to make the next step into our squad, and also to make plans and to create an environment that, let's say, avoids this year's problems in injuries."