Ian Madigan was the man who kicked both penalties for the Irish province, with the hosts' chances reduced further when Tom Ryder was sin-binned in the first half.
The result leaves the Warriors still firmly in the RaboDirect PRO12 play-off places, and despite failing to break down a resolute Leinster defence Townsend was quick to draw on the positives.
"I thought we defended very well in the first half but we didn't capitalise on the pressure we had in the second," he said.
"We dominated the territory in the second forty but found it difficult to string more than three phases of play together.
"We made some mistakes, whether of our own making or through the weather, but I thought it was a game we could have won."
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