Ramsey is expected to leave the Emirates as a free agent at the end of season after Arsenal withdrew their contract offer last month.
The Welsh midfielder has been linked with Chelsea and Manchester United, and Smith thinks they are making a huge mistake allowing him to leave.
“I think we all hoped this kind of situation would cease to happen with [head of recruitment Sven] Mislintat coming and [head of football Raul] Sanllehi,” Smith, who scored 115 goals for the Gunners, told Love Sport Radio.
“Maybe they arrived a little too late. I don’t know.
“It’s difficult to really speak without knowing the details but maybe Mesut Ozil’s vast salary is the reason they’re not prepared to put Ramsey anywhere near it and he’s not prepared to sign.
“But then again who is going to to give him that money? I don’t know.
“Where would he go? You would imagine his agent has already spoken to a few clubs so he’s got half an idea where he might end up.
“It would be a shame to lose him, it would be such a shame. I think, like a few players there, he can be developed into a top player.
“He’s pretty good as it is and he’s got this knack of scoring goals on the big stage and in important matches.
“It would be a blow if we lost him.”