Academy product Wood scored a third-minute try and Warrington loan forward Evans provided a strong performance up front as the Bulls scored 11 tries against their Championship One opponents.
Cummins, who side were beaten 36-6 at home by Wigan in the Super League last weekend, said: "Rochdale showed a lot of spirit, and we weren't far away. Last week we lost our way a little bit but we were better this week."
He added: "Our skill let us down for a few tries, but I was happy to see Ben Evans and Sam Wood out there, and both made their debuts and did well.
"I'm glad for Sam because he's been working hard, and he was able to go out there and show his skills.
"I was really pleased for Ben - that was his senior debut, and with the length of time he's been out I think he was a bit nervous.
"I don't think he slept much last night, but he enjoyed himself and gave a good account of himself."
Cummins is now looking forward to Monday afternoon's fifth-round draw.
"We'll see what the next round bring us, I'm happy to be in it," he added.
"We'd rather have an easier draw, but if you're going to win it you have to beat the best teams."
- Sports & Recreation