The Red Devils had several big chances during the game, but were unable to find the back of the net.
“It was a good performance, and it was just a shame we couldn’t score that all-important away goal because it could have been vital,” Giggs told the club’s official website.
“We completely outplayed them in the first half and we were really pleased with the performance. We knew they would come out strong in the second half but we were still able to create chances, which was pleasing.
“I thought we played well throughout, we looked good on the ball and there was great movement within the team. We felt confident and that showed in our performance.”
United will now have to beat Inter Milan at Old Trafford in order to progress to the quarter-finals of the Champions League.
“It’s still a tricky tie, and we would have liked to have scored that away goal,” he added. “But if we perform like we did tonight at Old Trafford then we’ll win.
“Experience is going to be very important. Inter are a top side and they have got goals in them. We will have to defend well and make sure we put our chances away.”