The centre scored two tries as Warriors overpowered the Dragons 47-17 to keep their faint hopes of a top-four finish alive.
"I think we have to win all of our games and we can do it," said Nick.
"Confidence is key and, with five points today, we're on the rise."
Glasgow head coach Gregor Townsend was pleased to see his side end a three-match losing run in the PRO12.
Speaking to BBC Scotland, Gregor said: "We got into our attack flow pretty well. When you're moving the ball so much, there will be mistakes, but we were working out where best to target in the Dragons defence. It was also fatiguing them as a side.
"Defensively, we just weren't in place in those first 10 minutes and they deserved their lead, but we showed really good resilience.
"The switch went on at 10-0. We won the kick-off back, got into their 22 and then eventually scored from the scrum.
"It was pleasing. I thought, individually, guys stood up really well. We showed the ambition we like to show when we play here."
The head coach echoed Nick Grigg's assertion that Glasgow can still make the top four but admits they will be relying on the teams above them to slip up.
"We could do with a 10-pointer one week," said Gregor. "We know we've got a lot of catching up to do and we'll probably have to rely on the teams above us losing.
"This is an exciting part of the season. We've got Connacht here in three weeks' time, a massive game against the champions.
"We'll have more players available and they'll come back (from Scotland duty) full of confidence."