The National League North Magpies won 3-1 but it wasn't a performance he will remember.
Jansen wants a run in the FA Cup but knows his team will need to do more in the next round than they didn't against Steve Burr's Evo-Stik NPL Premier strugglers.
"Stalybridge Celtic are a good side with good players and this was a potential banana skin for us," he told the club's autoboom.
"Having to play the last 15 minutes with ten men they threw everything at us and got a goal. It was backs to the wall but we managed to get the final goal and went through.
"I don't think we were firing on all cylinders. You need to approach every game the same way if it's Manchester United, Barcelona or the Dog and Duck. I demand that, and we started this match very flat.
"Of course we are happy to be through to the next round but I have told the players that I don't think we were brilliant, I think we were OK."