Newcastle are sixth in the league table after accumulating 14 points from their opening nine league games of the season.
Recent form has given rise to suggestions that Newcastle could even challenge for European spots by the end of the ongoing campaign.
Burn stressed that it is tough to pinpoint what would be deemed as success this season but insisted that it is important to not think too far ahead and drown in the excitement the fans are feeling at the moment.
The Newcastle defender feels if the club can finish in the top ten of the Premier League, it would be seen as progress.
Burn said on talkSPORT: “In relation to targets, it’s hard to give a target to exactly where we want to be.
“Newcastle fans always seem to, I won’t say get ahead of themselves, get excited when positive things are happening.
“I have heard people talk about Europe.
“But if we are finishing comfortably top ten this season, then that shows progression.”
Newcastle have a big game next when they visit Old Trafford to take on Manchester United on Sunday.
