Ole Gunnar Solskjaer's men became the first team to overturn a deficit of two or more goals in a home first leg of a Champions League tie and progress.
The draw for the last eight was not kind to United, handing them a two-legged tie against Barca but Smalling is adamant that is the sort of contest United players wanted.
"All our draws this season we don't have the easy draws, and we thrive off playing big teams like that," the centre-back told United's official magazine.
"After the PSG game, we know that we can go away to the big teams and get results. We're just looking forward to it. Let's take it on.
"We were warming up on the bikes in the gym [during the draw]. Normally we do 10 minutes on the bike and then we do some gym activation, but I think we stayed on the bikes for maybe 20 minutes just because we saw the draw was on the TV.
"We were all excited. As soon as it came out, we were all happy. We cheered and then we got on with training, but at least we knew who was in front of us.
"When the draw was made, you think, 'I want to play against teams like this'. I was injured or just coming back from being injured for the first game [against PSG], so it was nice to be able to test yourself against the best, and I think PSG is one of the best teams in the world."
United stunned European football when getting past Paris Saint-Germain in the last 16 as they progressed on away goals after drawing 3-3 on aggregate and welcome Barca to Old Trafford on Wednesday.
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