The Red Devils had to battle through a difficult first half, and were 2-1 down at half time to the Italian outfit.
But the home side showed their quality in the second period, scoring five unanswered goals to all but clinch a spot in the final.
"No, you don't feel the job is done but it was a good job done," Solskjaer told BT Sport.
"I think the character showed that they came back and didn't lose their heads.
"You could say we've got one foot [in the final], but you need two feet," he added, when speaking to MUTV.
"We're still halfway. A fantastic result to build on but you've got to be focused. I've seen stranger things. Football comes back to bite you if you take it too easily. We've just got to focus on Liverpool first and then Roma."