Old Trafford bore witness to an electrifying encounter on Saturday afternoon, when Andreas Pereira's stunner and a thumping Romelu Lukaku strike cancelled out an outrageous first-half effort by Yan Valery.
Frontman Sanchez suffered knee ligament damage in Saturday's 3-2 home win over Southampton and is facing several weeks out.
Pogba is unavailable for that match through suspension, so misses the chance to atone for the penalty he saw saved by Angus Gunn in stoppage time. "We have done it so many times before".
United appeared to be heading towards a disappointing home draw in the closing moments, when substitute Fred exchanged passes with Luke Shaw and found the in-form Lukaku on the edge of the area.
But it was seldom easy for City and manager Pep Guardiola was forced to replace Kevin De Bruyne and John Stones with muscle injuries that are particularly unwelcome with many important games coming up.
Already without Paul Pogba through suspension, Solskjaer will not be able to call upon United stars Ander Herrera, Anthony Martial or Jesse Lingard either.
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He said: "The dressing room was bouncing, they were happy, looking forward to Wednesday".
"We don't think if we win everything is flawless, or if we lose it is a disaster".
The Red Devils have won every one of their eight away matches under his leadership.
United leapt a point above the fifth-placed Gunners into fourth spot by beating Saints, and Solskjaer knows a repeat of January's FA Cup win at the Emirates will enhance their push for a Champions League finish. "It was like a two-second punch in the stomach when we conceded that second goal, it was a good goal too, which David [de Gea] had no chance with".
"We know it's going to be hard", the caretaker manager, who was also missing defensive trio Phil Jones, Matteo Darmian and Antonio Valencia at the weekend, told reporters.
"I just said to him there, "get ready for the next one, because you're going to take that as well", Solskjaer said. He was criticised for not letting Lukaku score, who was on a hattrick.
Five goals from 41 appearances across all competitions are not the kind of numbers English football fans have come to expect from Sanchez, who became one of the Premier League's most revered players during his four-year spell at the Emirates Stadium.