Thistle ended their long winless run with a 3-1 triumph over Aberdeen last weekend and head into today's clash with fellow relegation battlers Ross County ninth in the Premiership standings.
Archibald's side occupied the play-off spot for several weeks as their form faltered, but Bannigan reckons the gaffer's steely approach paid dividends for the Firhill outfit.
He said: "I don't think the manager panicked. He saw we just weren't getting the breaks.
"But he kept stressing to us that we had to step up and learn. Most of us are young boys, but he tried to drum into us that it wasn't an excuse any more.
"We have played enough games now to know what needs done at this level. He didn't buckle under the pressure, he is not that sort of man."
Thistle head to the Highlands today aiming for their second win of the season in Dingwall and bidding for back-to-back victories for the first time this term.
County boss Derek Adams took a cheap pop at striker Lyle Taylor in the aftermath of the 3-3 draw at Firhill last year, but Bannigan reckons the on-loan Sheffield United star has been the spark in the Jags' revival.
He said: "Lyle has been great, he has given us another dimension. Kris Doolan was fantastic for us in the first half of the season.
"Lyle has come in, he has got pace and he has got goals in him. He has certainly stepped up to the plate in the last couple of weeks
"He has pace and power and he causes defences all sorts of problems. Aberdeen have a big, strong, experienced defence and he could have scored four or five in that game. He can cause havoc to a lot of defences.
"He isolates himself and gets himself one on one with defenders a lot. His pace can take him away from most people."
Taylor was the Jags hero last weekend as his secondhalf double put the in-form Dons to the sword in Glasgow, but the striker is not the only Thistle star to impress this term.
Bannigan has looked back to his best after a frustrating few weeks and the midfielder reckons he has found his feet in Scotland's top flight.
He said: "I am starting to feel [like I belong here] now. I started quite well and then faded away around October/November time.
"I feel I have started to come into my game in the last few games. It takes a while to get used to, but I feel I am getting there now."