Both players found the net in the space of 82 first-half seconds as Chelsea claimed their second successive win in all competitions for the first time since the end of August.
"For 'Mischa' he scored his first goal in the Premier League, and for Armando after a long period out, he scored again. I’m so happy for them, they deserve it," Pochettino told the club's official website.
"We need to understand that young people need time and need to settle. It’s about adaptation.
"It’s a big change when Mudryk arrived here and when you arrive at a team, it’s not easy to settle in a team that isn’t solid. He wasn’t the cherry on the cake, they needed to add something to the team.
"It’s about time, having patience, trusting these young talented players, building confidence. It’s a big job, step by step. Sometimes people don’t have the patience but for us it’s about having the patience. Even when we weren’t winning, we were calm, stayed positive, had the belief."
Injury update on Mudryk and Caicedo
The victory could have come at a cost, though, with Pochettino revealing that both Mudryk and Moises Caicedo had picked up injuries.
The former didn't appear for the second half, while Caicedo was withdrawn in the final moments at Craven Cottage.
"He [Mudryk] felt something in his quad, which we need to assess. He didn’t feel comfortable to keep playing. We hope it’s not a big issue, we hope it’s nothing big and he can be available for Saturday," Pochettino explained.
Regarding Caicedo's fitness, the Blues head coach added: "It was a contusion. Hopefully it’s nothing serious, he was tired and we will see."
Up next for Chelsea is a trip to Burnley, who are still seeking their first win of the season, on Saturday.