The Dutch side, who already knocked Tottenham Hotspur out of the competition in order to reach this stage, will host Jose Mourinho's men on March 10 - with the second leg taking place at the Stadio Olimpico a week later.
Letsch acknowledged that Roma will go into the tie as favourites, but pointed out his side have already upset the form book in the competition this season.
“I really like the draw, I think the whole team like it,” Letsch said.
“Of course it is the toughest opponent we could get, but in the end it is exactly what we would have wanted.
"At the beginning of the competition I heard a lot of people doubting what the Conference League was – 'What sort of competition is it, really?' - but we’ve had Tottenham, Stade Rennais and now AS Roma. So it’s a great competition and we have nothing to lose.
"Of course they are a big favourite, and personally I look forward to going up against Jose Mourinho because he is one of the greatest coaches around. So, yes, it’s a fine draw.”
Vitesse beat Rapid Vienna in the play-off in order to get to this stage of the competition, after finishing second in their group behind Stade Rennais.
They currently sit sixth in the Eredivisie standings.
"At the moment we will focus on [our next game against} NEC but of course we know Jose Mourinho’s qualities and preferences with his other teams and now with Roma," he said.
"At the beginning of the competition Tottenham were the club with the most valuable squad – and we kicked them out. Now it is Roma, so Roma is one of the big favourites of the competition. So there is nothing to lose, but we will have a chance.
"We are one of the teams that has shown that anything is possible in this competition. Bodo/Glimt are another, so hopefully we will have a full stadium for [the first leg at home] and make it a special night.”
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