Sancho completed a £73m move from Borussia Dortmund to Old Trafford, signing an initial five-year contract this summer.
The 21-year-old has had a slow start on his return to English football, having failed to record a goal or assist in any of his six appearances across all competitions.
Sancho has made two starts in the Premier League and was brought on for the final 17 minutes in the 2-1 win at West Ham United over the weekend.
Keane admits that expectations are high following the big-money move but wants Sancho to be given the opportunity to settle.
"He'll be fine," the former United skipper said on Sky Sports.
"He's been at the club what, two months. There's been a lot of changes, new players coming to the club – give the kid a break.
"He's still learning his trade, he's still a young player, big expectations.
"He's come to a new club where he's certainly not going to be star man, he'll be down the pecking order and he's got to adapt to all that. Give him a chance."
