The Scots found themselves down to 13 men after Simon Taylor and Andrew Mower were sin-binned but battled bravely to repel England whilst outnumbered.
McGeechan said: "If you are going to beat top sides and stay there, consistency as a team and an individual is one of the important things.
"We knew we had to be competitive through the game against England.
"They might not have anticipated the score being so close but that is how you put pressure on them - by keeping the scoreline close.
"I'm always trying to work on being as competitive a unit as we can be. We'd all like to see the opportunities come out of that competitiveness.
"You don't know when they will come but you have to be in a position where you can take them and not be afraid of taking them."
McGeechan hopes the never-say-die spirit shown at Twickenham will be evident again at Murrayfield.
"I wish our pack could always play as though they had six men because they were excellent and our half-backs made very good decisions to make it easy for our pack to play.
"Sometimes, by default, you get an understanding of the intensity and the level you want to be working."