United defeated rivals Manchester City on Saturday to move up to fifth on the Premier League table.
"In all big games you need that concentration and that's what the players had today," said Giggs.
"They had that concentration, both defensively and when they won the ball.
"Making sure that that pass forward was good, the touch was good, and players flying off Anthony Martial and causing City big problems.
"We all know United's record against the big teams and when the big teams open up we can expose them on the counter-attack.
"The next step is breaking teams down, and that's why we have to get Paul Pogba back. He's the one who can unlock the door. Get him back playing well and consistently because that's the next step then.
"I think every team above United, we're unbeaten against. It's the teams below that make it difficult at Old Trafford. Where you've got to be patient, that's the next step now. But that was a fantastic performance. The best performance I've seen in a long time from a United team."