BO Henriksen admitted Kidderminster Harriers were "quite happy" after extending their unbeaten Division Three run to three games.
Harriers were poised to take all three points at one stage due to Henriksen's 49th-minute penalty.
But Bury did enough to warrant their equaliser from Jon Newby on 77 minutes.
Harriers had previously recorded two victories over Leyton Orient and at Wrexham.
Henriksen said: "To be honest I think 1-1 is fair enough. To be fair to Bury they are a good side. They want to play the ball around.
"I didn't play my best game but there were one or two situations in the second half where I could have put one more goal in.
"But we have got a point and we are quite happy with that.
"After the first half-an-hour we started to play a bit more and show what we are capable of doing."
Harriers boss Ian Britton echoed Henriksen's sentiments but admitted: "I had a bit of a go at them in the dressing room after the game.
"All three points were there for the taking and then we've gone and thrown two away near the end.
"The conditions made it difficult to produce the type of football we like to play.
"We made the mistake of playing too much in front of them in the first half.
"But when we got the ball in behind the defence in the second half we started to cause them a few problems.
"We weathered the early pressure and even though they had a lot of the ball they didn't really do a lot with it."
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