Rashford, on-loan from Manchester United at Barcelona this season, has broken back into the England squad for this week's internationals.
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Gascoigne told talkSPORT: "I like Rashford. I just wish he would smile now and again. It winds me up.
"Like when you score, smile at least, because you've got a bloke that's got three kids and he takes them to the match.
"It costs a lot of money. They all want England shirts. It costs money. They want food. It costs money.
"Then he probably gets home about three or four o'clock in the morning after driving home, but the players are back home at half eleven getting massive wages.
"If you're going to score, please at least celebrate. Have fun."