Sanchez agreed a season-long loan deal with the San Siro outfit on Thursday after failing to settle in his 19 months at Old Trafford since being signed from Arsenal.
And his exit means United will have to cope with Anthony Martial, Marcus Rashford and 17-year-old Mason Greenwood as their only senior centre-forward options for at least the first half of the Premier League season.
The United manager said on Friday that he would ideally have been able to bring in a new striking option during the summer transfer window, but the club were unable to get the target they had identified.
“At the moment we’re creating chances, but of course we’re always looking for someone to improve us, and we did and we were looking,” Solskjaer told a pre-match press conference.
“As I said on the way back from tour, we were still looking for a replacement for Romelu if he went. We’re one down, to be fair, but we didn’t find the right one and we didn’t get the answer we wanted.”
Martial’s current thigh injury sees him miss Saturday’s trip to Southampton, opening the door for Greenwood to potential make only his second senior start.
But Solskjaer added that while he has faith in the youngster’s quality, the Reds could do with another striker with qualities similar to those which made the manager himself famous.
“Mason’s a natural footballer, he’s enjoying his time on the pitch. He comes alive when he gets closer to the goal, which is great to see, and the finishing sessions he’s always the one who ends up in the last two, he always scores the most,” said Solskjaer.
“He’s not scoring scrappy goals, I’ve got to say, he’s got proper goalscorer goals. And he also has to learn that scrappy in the six-yard box, and stick your head in where it hurts. But he’s got the whole range of finishes.
“I do like the one who scores scrappy goals, in and around the box, a young Ole or something! It doesn’t have to be a 1.95m centre forward, no. But sometimes you think if we want to play with two up, maybe a different type to what we have.”
The Norwegian says the decision to allow Sanchez to leave for the season came after an honest conversation between the pair, but he expects the 30-year-old to still have a part to play for United despite having netted only five times in 45 games for the club.
“I had a chat with him, and for me if I can’t guarantee regular football for Alexis Sanchez it’s better for the two of us that he goes and plays in Italy and shows what we know he’s capable of. But I wasn’t prepared to guarantee that.
“I’m sure we’ll see Alexis back, we just hope he plays regular football for a year now and he can find his form. This is a loan for a year, Chris Smalling’s Roma deal is a loan for a year. We expect them to be professional, go there and represent Man United as well, and we want them to do well.”