Pools beat Huddersfield 3-1 on Saturday to ease their relegation fears, but Stephenson knows more is required to keep the Monkey Hangers from slipping back into the drop zone.
He said: "We are unbeaten in five games now, and we've shown what we can do against teams much higher up the table.
"It's important we build on this now and carry on climbing up the table, starting at Scunthorpe on Tuesday night."
The win at the Galpharm Stadium helped Pools up to 17th in the table, three points away from danger.
Stephenson added: "That was a great win, a great performance, and we scored three great goals. We've been practising our finishing in training this week, and it showed.
"I'm delighted for the players, because they won that game against a side going for promotion on merit. They've all been brilliant since I was put in charge, and this is their reward for some hard work and some great football."