will this above mistake will slowdown my application in the further course of the day .
Does piling of such unclosed database connection can make my application slow ?
Not on its own. The connections will keep hold of resources that can't be garbage collected and will keep hold of database resources, so you will run out of available database connections. I'd expect to se a steady increase in memory used, which may or may not slow it down, then exceptions once there are no available connections left.