Cork, who returned to the starting line-up after a two-week recovery from injury, insists there is still plenty to play for between now and the end of the season.
He said: “We’ve got Newcastle next week so if we beat them then everything is back to how it was. That’s a massive game for us.
“People look at us in the table and say we haven’t got much to play for, but we can now try and get above Newcastle, and then look at the teams above them.
“We’ve got Manchester United in the last game of the season, so until then we have plenty to play for.”
For the second time this season, Saints threw away a lead before losing 3-2 to Spurs. But this time they squandered a 2-0 advantage.
“It’s quite hard to take,” said Cork, “we were 2-0 up and quite comfortable. “We talked about a few things before the game, stuck to the plan and it worked well as we got a good 2-0 lead. And then two mistakes got them right back in it.
“The third goal was a little bit cruel, all the lads are gutted, especially after being in such a good position.”
Cork acknowledged that Spurs scored their goals at a crucial time.
He said: “It’s difficult when the other team comes out at half-time and they get a goal so quickly. “We said at half-time that we needed to be right on it. You can say it, but sometimes you’re not ready for it and they scored straightaway which made the second half difficult for us.
“When we talked about this game, we knew what we wanted to do by getting in behind the centre halves and playing in the channels. “It did work, but unfortunately they pressed a bit higher in the second half and made us sit a little bit deeper which made it harder for us.”