Welsh winger is frustrated that Red Devils fail to punish German side to a greater degree as Alex Ferguson's side are stifled by Manuel Neuer in Gelsenkirchen.
The Welshman got the first goal of a game which United dominated and could have secured the tie had it not been for a string of fine saves from the hosts' goalkeeper Manuel Neuer.
“We created enough chances to be four or five up,” Giggs admitted to Sky Sports.
“Before the game we would have taken 2-0, but we are a little disappointed to be only 2-0 up.”
Wayne Rooney added the second of the night to give Sir Alex Ferguson’s side a comfortable lead heading into the second leg at Old Trafford and the striker revealed he was pleased with his side's display.
“Overall we’re pleased with the performance with two away goals, it’s a good away win for us. So we just have to be professional and finish the job at home," said Rooney.
Rooney was clear that United would have to concentrate to ensure they reach the Wembley final next month.
“Schalke are a good team and you can’t take them lightly. They won 5-2 at Inter so we have to be professional,” he said.
Giggs’ goal meant, at 37, he is the oldest goal scorer in the history of the Champions League his response after being told of the new record, he replied, "Thanks for that, great stat.”