The Scots had played some entertaining rugby in the first half but, after a spirited Italian fightback, McGeechan's men were hanging on in the end for a 33-25 victory.
However, the Scots coach insisted there were plenty of positives to be taken from the game.
He said: "I think we could have scored 20 more points in the first half because we had three or four good scoring opportunities.
"We picked a plan to attack and we were finding holes in their defence. We didn't have to force it and we were working in the areas where we wanted to go.
"That's what pleased me most about the game. In the second half we didn't play anything like that so it's all credit to the players for their defending.
"We spent a lot of the time without the ball and then we had to come back later on in the game but we shouldn't have to do that."
Scotland captain Bryan Redpath heaped praise on team-mate Chris Paterson after an impressive performance by the Edinburgh player.
He said: "Chris finished his second half try off exceptionally well and also his penalty after that.
"He's worked a lot on his kicking and he gave us the breathing space which we needed at that time."