Danny Welbeck netted in the 20th minute to give the visitors a lead at the Bernabéu before former United forward Cristiano Ronaldo equalised with a powerful header.
Sir Alex Ferguson’s side held on to secure a 1-1 draw ahead of the return leg at Old Trafford on 5 March, and Giggs believes Welbeck’s strike could prove crucial.
“There’s plenty of positives. It’s obviously a good result,” Giggs told Sky Sports.
“We scored the goal – which is always important, getting that away goal – and we defended really well, so we’re relatively happy.
“The team that we picked, we had goals in us, and that’s what we tried to do, score goals and create chances.”
Ferguson’s decision to pick Welbeck was a surprise after the England international’s struggles this season – the 22-year-old had scored once in 27 appearances prior to the second-round clash.
And Giggs heaped praise on the United youngster for an impressive performance against the La Liga champions, which the striker capped with his first-half strike.
“He was brilliant all night, Danny,” added Giggs.
“He was causing them all sorts of problems. He deserved the goal.”