Spurs made light of their gruelling schedule by beating Frank Lampard's men 5-4 on penalties after the match ended 1-1 after 90 minutes in north London.
They were back in action just 48 hours after playing Newcastle in the Premier League and take to the field again on Thursday in the Europa League.
Alderweireld said, "I think we really worked hard for the result.
"Second half was very good. Of course, we have an unbelievable team but we have a lot of games this week, so we played with another team.
"But we showed we have a big squad and we had to grind out the result. Okay we didn't win the competition but this is a big step.
"We'll take it game by game but for the morale it's very big to win this type of game."
Alderweireld believes the current schedule puts the players at risk.
"We don't want to complain, but of course it's not easy to play every 48 hours," he said. "It demands a lot from the body, even a little risk.
"But everyone works so hard for it. Today, especially second half we worked so much better, we pressed them and we could have won it. When you get the penalties it's always a bit lucky and today we were on the good side.
"The only thing that compares is (the) Christmas (schedule). This is very tough and again a little bit risky for injuries.
"It's not only tough in your mind but also your muscles. You're playing one of the biggest teams at a Premier League tempo, so it demands a lot on the body. We try to get through it in the best way possible."