The Reds will meet Eusebio Di Francesco's men in the last four, with Bayern Munich taking on holders Real Madrid in the other match-up.
Roma produced a stunning second-leg performance to knock Barcelona out at the quarter-final stage, but they were largely regarded as the preferable opponent heading into Friday's draw in Nyon.
Klopp, however, does not think anyone who watched the matches against the Catalans could consider Liverpool to be fortunate.
"It was not that I thought 'thank God not Bayern, thank God not Real Madrid, yippee Roma' or the other way around," he told the club's official website.
"It is just the draw and I know it is very exciting, but it is good because the most important news is we are still in the competition. Whichever opponent we would have got, I would have said there is a chance because it is football – so there is a chance against Roma.
"But if anybody thinks this is the easiest draw then I cannot help this person; they obviously didn't see both games against Barcelona. In the first result, the 4-1, it was not like the game was – it was [Lionel] Messi genius against a good side of Roma. The second leg was outstanding, it was outstanding what they did. They should have probably won four or five-nil – I was really impressed.
"It is work and no problem with that and now we are looking forward of course to the first game."
The tie will see Mohamed Salah face his old club for the first time since his transfer to Anfield last June for an initial fee of €42 million.
Klopp believes Roma have underlined their quality by reaching the semi-finals, despite losing a player who has managed 39 goals and 11 assists in his first season with Liverpool.
"For sure it will be interesting for Mo, but that shows all the quality of Roma," he said. "Everybody knows how big Mo's impact on our season has been – and they've played a season without him. Where would they be if Mo was still there?
"It makes it a really interesting thing and for him, it will be 100 per cent special. He is already of interest wherever we go, but it might go crazy when we go to Rome! He can deal with that, I am sure."