The former Arsenal boss even suggested that the Merseyside club could drop points in their next match against Newcastle next at St. James' Park, with City facing Leicester at the Etihad.
The Wales global will therefore be denied a send-off appearance for the Gunners, having agreed to join Juventus when he becomes a free agent in the summer.
"We'll miss him", added Özil.
The Welshman suffered a hamstring tear during the Europa League quarter-final against Napoli a fortnight ago - but hoped he might be fit in time to play in the second leg of the semi-final against Valencia. The 26-year-old midfielder did not play during the battle with fellow Top Four contenders Chelsea and last featured in a Red Devils shirt against Manchester City last Wednesday.
"We need to focus on our two games, win games again", said Solskjaer, but a big rebuilding job remains ahead for the Norwegian.
"I don't think he can contribute enough to Arsenal".
"I wanted to enjoy with him. He is not on the pitch but he is with us".
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And in truth it's probably a good thing, because he was 100 percent correct in his assessment of the club, and they are views that a significant number of fans of the club will echo.
And the defender hailed Ramsey's attitude since his move to Juventus was announced.
After being named Manchester United's Player of the Year for four of the past five seasons, the 28-year-old has now made three errors leading to goals in his last four matches.
"All we have done for the past two seasons, nobody gave us anything. we won it, we did it and that's good. It shows a great mentality and character".
However, doubts remain over his ability to lead Arsenal's rebuild back to the heights they once enjoyed under Wenger.
The Wales global etched his name into Arsenal folklore by scoring the winning goal in Arsenal's 3-2 FA Cup final win over Hull City in 2014.