The Magpies' best chance fell to defender David Rozehnal and Allardyce admitted: "It was frustrating in the end that we failed to break down a very solid defence.
"All we needed was to pull something out of the bag to win the game 1-0 and we haven't quite managed that but it was very important to keep a clean sheet and that makes me very happy.
Villa boss Martin O'Neill was pleased with his side's performance but admitted his disappointment not to leave with all three points after a bright display.
O'Neill said: "I thought we were the better side and it was a really good performance. The players were very strong and very determined and we should have won it.
"We got a point to show for it but we are very disappointed in the dressing room that we haven't taken it. There was a bit of pressure to get something today hence that disappointment.
"With it being Newcastle's opening fixture at St James', you might have been tempted to say let's just get something, but the way it went we are disappointed."