The Saints, who were held to a 1-1 draw at home to Swansea on Saturday, have endured a frustrating return to the Premier League having only picked up one win in their first 11 games.
Cork made his first Premier League appearance of the season on Saturday following an ankle injury and believes that the good atmosphere among the squad can help turn their fortunes.
He said: "We went to a hotel about an hour away. We had a bit of training at Aldershot on the first day. Then we went clay pigeon shooting and had a bit of team bonding. Jason Puncheon must have cheated as he got the best score. But it was good for the lads to get our heads around it.
"It gave us another chance to really think about tactics and get our heads really on the game, go back to our rooms and get our heads down.
"I've done clay pigeon before but not which such a lot of lads. All of the lads loved it. Emmanuel Mayuka was last and he had to be Punchy's slave - he had to get his dinner for him and stuff like that."
Former Chelsea midfielder Cork also believes that the Saints aren't feeling any pressure just yet, adding: "We talked about it quite a lot over the last week or so. There's no pressure on us now, we just have to go out there and play how we know we can.
"We've had a great couple of years. This is one of those ones years when things aren't going our way. Now we'll find out what we're really made of and try to get the results going again.
"We had the winning mentality for the last two years, so there's no reason why we should just suddenly lose it.
"We're down at the bottom but I don't think there's any pressure on us at the minute. As long as we can keep playing well, hopefully that'll get us up the table."