Saturday`s 2-1 win against Crystal Palace was enough to lift United into sixth place and with the hectic Christmas period coming up, the next month will start to shape the division.
"We`ve done well these past few weeks and we`ve got ourselves in a strong position," said Grayson.
"On Saturday we showed some real characteristics and belief.
"Whatever we achieve will be a real team effort.
"A few weeks ago we challenged the players to go on an unbeaten run and they`ve done that.
"What we have to do now is maintain and improve on that going up against Burnley."