Castellanos struck the winner in the eighth minute of extra-time.
“I’m very happy,” Taty told West Ham TV. “We knew it was a very important match for us, for the team’s confidence.
“I think we’ve done a really good job. I’m very happy about my first goal in this shirt; I felt really good and very pleased.
“It really is very important given the situation we’re going through. This is about working day after day, training session after training session. That’s the goal; in the end, we all have to do things right together and keep working on this growth, which will be good for everyone.
“I’m really happy about scoring. This kind of victory is always good for the team and will give us a much-needed boost for the rest of the league season.”
Next up for West Ham is Tottenham, where Castellanos will face fellow Argentine and Spurs captain Cristian Romero.
He added, “All matches are important, and we have to approach them with a lot of responsibility, representing this jersey.
“Now we’re preparing for this very important match against Tottenham, and it’s going to be a great duel with Cristian as well.”