Saints upset the reigning champions to claim their first win of the Clydesdale Bank Premier League season and move off the foot of the table on Saturday.
Vine's goal was his first for the club while Tade netted for the first time in the SPL, having opened his club account in the Europa League second qualifying round against Eskisehirspor.
The McDiarmid Park result was even more of a shock given the virus which has swept through Steve Lomas' squad this week, but Tade told ESPN: "You play to win games, every time.
"Even though we've been hit with a bug this week and most of the boys were not feeling well, the gaffer said that's no excuse.
"We needed to approach the game in the right manner and we did that, and we won the game.
"When you're a striker you need to score goals, that's the bottom line. I knew we had goals in us, with Viney and Nigel (Hasselbaink) and myself, and today we delivered."
Vine agreed: "Competition's great for everyone. Myself and Greg have only played two or three times together and I'm confident that when Beatts (Craig Beattie) is fit, and Macca's (Steven MacLean) a little bit fitter, we're going places."
The former QPR and Luton striker announced himself to the McDiarmid Park faithful with a pre-season brace against Bristol City but he said: "That was only a pre-season friendly - today's a little bit more special."
Celtic boss Neil Lennon, who saw his side throw away a lead given to them by Kris Commons, said: "I'm disappointed. We got off to a great start and let the game get away.
"We didn't do the basics well enough, far too many were out of form. We had chances in the second half but we didn't compete well enough.
"Credit has to go to St Johnstone but we didn't play well enough. I don't think it was complacency but it wasn't the quality I expect from these players.
"Maybe the international break came at a bad time but we played like strangers at times today."
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