The experienced Scot, who is set to tour for a sixth time (twice as a player (1971, 1974) and four times as a coach (1989, 1993, 1997, 2005) with the Lions, was not about to panic after he watched Jonny Wilkinson rescue a draw with his sixth penalty kick in injury-time.
McGeechan said: "It's early days - that's (six days) the shortest time any Lions team has had to prepare from scratch and the more understanding we get the calmer we will get.
"We had to work hard for all we got. We probably got a bit over-excited when we did get some space. We didn't get the quick ball we wanted so we tried to force it too quickly.
"It's given us a pointer to the accuracy we will need in New Zealand."
New Zealand assistant coach Wayne Smith, who was adopting a watching brief for All-Blacks boss Graham Henry, also failed to draw many conclusions from a poor Lions display.
"Wilkinson was very good, they would be very pleased with how he made it through. He didn't shy away from anything physical at all. He's back - he enters the contest now."
One man who was clearly not afraid to stoke the fires ahead of the three New Zealand-v-Lions match-ups on June 25, July 2 and July 9, was former All-Black prop Craig Dowd.
He told Sky Sports News after viewing the Pumas game: "There could be a few New Zealanders waking up to that game, probably chuckling to themselves, thinking the Lions aren't all that.
"But if we put things into perspective, it was the first game off, there were going to be inaccuracies and they will improve.
Dowd added: "I think they saw Argentina and thought 'we'll beat them, 50 points - it should be a walk in the park', and they didn't give Argentina the respect that they truly deserved."