The England goalkeeper added the team are determined achieve a higher level of consistency as he targeted a second straight Premier League success when Wolverhampton Wanderers visit Goodison Park on Saturday.
Richarlison’s third-minute strike proved decisive against the Terriers – the Brazilian slotting home at the second time of asking after Jonas Lossl repelled his initial effort.
Lucas Digne was sent off after 66 minutes but Everton defended impressively to secure maximum points.
Pickford admitted it was vital for the Blues to hit back immediately after the disappointment of Saturday’s FA Cup exit at Millwall.
The win over Huddersfield lifts Marco Silva’s team into eighth in the table and Pickford hopes the result can ignite a positive run of form.
“I think we showed a lot of character [against Huddersfield],” he said. “Now we need to step up and keep that level high.
“We’ve got to go into every game and be resilient as a unit. We kept a clean sheet and a lot of hard work went into it.
“We were very disappointed at the weekend to go out of the Cup, as a group of players and as a club we wanted to go further than we did.
“But the important thing was to bounce back and I think we showed character and got the win.
“Now it’s about finishing as high up the table as we can. We know it’s going to be tough but it’s all about going on a good run.
“We want to get back-to-back wins and go on a run. We’ve been a bit too inconsistent this season and we need to get that consistency level up.”
Everton got off to a flying start against Huddersfield, who were under the stewardship of German manager Jan Siewert for the first time.
Richarlison's early strike came after excellent work from Tom Davies, who impressed throughout at the John Smith’s Stadium.
The Blues continued to carry the greater threat, circulating the ball with speed and conviction and regularly advancing into threatening positions.
While the game took on a completely different complexion when substitute Digne was sent off on 66 minutes, Everton defended resolutely as the home side exerted increasing pressure.
When Huddersfield were able to fashion any opportunities, they found Pickford in stunning form.
The 24-year-old first beat away Aaron Mooy’s free-kick effort, before making a fabulous, sprawling stop to keep out Elias Kachunga’s powerful header.
“They were decent saves,” Pickford said. “With the free-kick, they had about four players in front [blocking my vision] so I didn’t see it until late, and I’ve made a good stop.
“The second one, he’s made a good header, but I was in the right position.
“I’ve moved my feet, I’m very fast around the goal and I’ve got a good hand on it in the bottom corner.
“It’s part of my job. I think they’re not two worldy saves, they’re two good saves. It’s all about where I am in the goal. I train hard and I know when to get in the right positions at the right time to give myself the best opportunity to make the save, which I felt like I did.
“The clean sheet was important but it’s not just because of me, it’s the whole team. It starts at the top of the pitch and the gameplan we set up. We work hard as a unit.”