After limping to victory over The Borders last week, Glasgow ground out a 12-10 victory over Edinburgh at Old Anniesland on Saturday.
Edinburgh had the bulk of possession and territory but all too often found their efforts snuffed out by excellent defensive work from Glasgow.
In today's Daily Record, Kenny said: "We won ugly against the Borders and now we have won ugly against the Gunners - and we will be quite happy to keep playing ugly if it means we're winning.
"You can build on ugly wins but it is very difficult to use defeats as a springboard to anything. Success at this level is based on defence and this was the perfect example of winning because we were tight at the back."
Hugh Campbell, the Glasgow coach, was not getting carried away, telling today's copy of The Scotsman: "It's not pretty right now, but there is a lot more to come from this team. We weren't secure on our own ball all night, we kicked it away at the wrong times and lost ball in contact too often, and you can't carve out opportunities when you do that.
"But we did it the hard way. We have focused the first part of the season on defence and involved some of the senior players in helping drive that. We don't have a lot of time at the moment with the players, but every single session we're doing defence, at the expense of some other things, because if you get your defence right then you can build on that.
"The spirit, guts and determination to win that game against the odds was just outstanding and I feel it is a good omen for Glasgow rugby."
Glasgow skipper Jon Petrie said: "It was a huge effort from everyone but we can't keep relying on the misfortune of the opposition. We have to start putting teams away."