It was a frustrating first game at the helm for the former Borussia Dortmund reserves boss, with Richarlison's third-minute penalty proving decisive for the Toffees.
But Pickford's display for Everton, who saw substitute Lucas Digne sent off, was also key as he made two stunning second-half stops to deny Aaron Mooy and Elias Kachunga.
"I saw why Pickford is England's number one with incredible saves," said Siewert, whose side sit bottom and 11 points from Premier League safety.
"We shouldn't find excuses. We need to focus. It's a process which has started. I saw many things I implemented in training.
"The most important thing is we create chances and the goals will come. The lads got my ideas and we had chances."
Not the start Jan Siewert had in mind as a sole Richarlison strike in the opening minutes condemned #htafc to defeat against @Everton on a bitterly cold Tuesday night in HD1.— Huddersfield Town (@htafcdotcom) January 29, 2019
https://t.co/4OssGFCEp3 #HUDEVE (AT) pic.twitter.com/JODmqCabeZ
Silva also had words of praise for Pickford and acknowledged it was an important win for the Toffees, who climbed to eighth.
"The main thing was to win, to do everything to get the three points and to give a big answer to ourselves and our fans," he said.
"Three points away from home and a clean sheet was important to boost our confidence. It was difficult with 10 men, having played a game on Saturday. They had 10 days to prepare. It was well deserved for our players.
"One free-kick, one header, but they didn't create anything more. Jordan did well in those two moments."