The Scots have opened their World Cup campaign with two wins, and claimed victory in persistent rain on Wednesday that had a huge influence on the game.
"The conditions dictated a lot of today," Lawson said on ITV.
"We came up against a big old Georgian side who were really determined, really physical, and ultimately it was a workmanlike performance to put them away today."
Scotland's defence had come under fire after Saturday's 34-24 win over Romania, but Scotland looked much more solid at the back on Wednesday.
"That adds to a little bit of tension," Lawson said of the criticism.
"But we just kept plugging away in the right areas and then took the points when they were on offer.
"It's a massive hats off to our front five today. They took the Georgian scrum on. A lot has been touched on there but the boys went out and showed what we're about today.
"We came here looking to get two wins and it's tough with a four-day turn around, but we got what we came for. Now we prepare for the next challenge."
Scotland coach Andy Robinson was disappointed with the number of turnovers, but praised the defensive improvements since the weekend.
"It wasn't going to be pretty at times with the weather and we needed our front five to perform tonight," he said.
"I thought they did that really well.
"Because we turned the ball over we allowed Georgia to get out of their territory.
"But I was really delighted with the way we defended. We had to step up from last week when we conceded 24 points. That was very disappointing, so it was pleasing to see this. The four-day turnaround was tough as well.
"When we came in to Invercargill we wanted nine points minimum so I'm really pleased we've got those nine points.
Georgia's Scottish coach Richie Dixon admitted his side needed to cut out on mental errors to get results.
"I think over the game Scotland dominated in attacking us," he said.
"Our defence was coping but unfortunately for us there were too many errors and Scotland kept us from getting any momentum.
"You can do all the training you like but it's only in the first game that you really find out so we know we have a lot of work to do.
"We killed ourselves in terms of attacking momentum with so many fouls and penalties."
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