McGeechan was pleased to see significant improvements from the 19-13 Hamilton loss, especially at breakdown and contact areas where veteran flanker Neil Back was at his bustling best.
"We are pleased with the control of the game. I thought the pack played very well and we were just one pass away from some fairly significant scores," he said.
"There are still things to work on but I think there were some significant steps forward in the contact area and our support work.
"I don't think the weather or the pitch was conducive to strong back-play. Doing the same things in drier conditions and with drier hands, we would probably have got players free.
"I don't think the All Blacks would have got any more control of the game than we had."
The Lions established a 13-6 interval lead thanks to Gethin Jenkins' 15-metre dash for glory following an incisive break from scrum-half Dwayne Peel and perfectly-timed Martin Corry pass.
They then scored only three more points until the 78th minute, when Thomas marked his first tour start by perfectly executing a kick-and-chase try.
McGeechan's coaching colleague Gareth Jenkins was particularly impressed with Back's contribution.
"I thought Neil Back played very well," he said.
"He's got huge experience and he brought that to the fore today. I thought he fronted up and he's proved to us he is ready, if he is selected, to play Test rugby.
"As for Gethin Jenkins, I thought he was man of the match. He proved to everyone in New Zealand what type of player he is, and showed the form he has been producing in the northern hemisphere."