The Red Devils had Jose Mourinho's side on the back foot in the opening 45 minutes at the San Siro in the first leg of their UEFA Champions League clash on Tuesday.
Julio Cesar was the far busier keeper on the night, especially in the first half, but Sir Alex Ferguson's troops 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.
Outplayed them"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."
All United need to do to progress to the quarter-finals of the competition is beat the Serie A leaders on home soil, but Giggs believes the tie remains finely poised.
"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."