Cristiano Ronaldo and Wayne Rooney grabbed the goals for the visitors, but Spalletti declared afterwards: "If you look at the result they are certainly of a different class, but if you watch the game then that is not the case.
"The only thing I really didn't like was the way we conceded the second goal and after that the lads lost faith in their own abilities and chances of turning this around.
"In my view, we played the way we had to. We certainly deserved more, especially in the opening 20 minutes of the second half.
He continued: "It is United's work rate and willingness of every player to sacrifice themselves for the defensive movement that makes the difference. They maintain a balance between coming back to defend and leaving space to run forward without getting tired.
"They have great stamina and individual talent, although I must point out tonight they were rather fortunate. The talent is there, but so is the luck!
"I said in the Press Conference yesterday that people always maintain Italian clubs play defensive and on the counter, so in that case Manchester United are the most Italian team I know!
"I've seen at least 10 of their games and they always play like this. They sit back, soak up pressure, clam up in midfield - which unfortunately we allowed them to do and play between the lines - and then break forward on the counter.
"We played our game and did what we had do, although obviously the team got depressed when United scored with their first foray into the penalty area.
"We were unlucky on a few occasions and consequently must accept the situation and try to turn it around."
The 2-0 home defeat in the first leg is a damning result, especially as last season Roma lost 7-1 at Old Trafford.
"Admittedly it's very difficult, but we must not make the mistake of assuming we are already out. After all, we have scored two goals in places like Lyon and Madrid," noted Spalletti.
"When United took the lead we tried to push 10 metres further forward and we did put them under pressure, but couldn't take our chances.
"I was very unhappy with the last 10 minutes, when we were very disconnected and sent out the wrong message. I never want to see that approach again."