The Spanish giants boosted their hopes of reaching the knockout stages with a 3-2 win at Atalanta on Tuesday (10.12.24) and Bellingham was happy to get a win on the board after the club experienced a difficult start in the defence of their trophy.
Asked for his overriding emotion after the match, he said: "Probably relief. I think it was really important for us to get the points tonight.
"It was a really difficult game. We knew coming in how difficult it would be with their style of play and the atmosphere inside the stadium, so it was important that we got over the line."
Madrid are now 18th in the 36-team league and Bellingham hopes that Real can make up the three-point gap to the top eight so they won't have to be involved in a knockout play-off in February - which would add two more games to an already busy season that sees them travel to Qatar next week for the FIFA Intercontinental Cup.
The England midfielder said: "It's less games, it's more rest for us and it's a chance to regroup a little bit.
"We've got a tough schedule, we've had a really tough schedule, with a lot of away games.
"I think now we're away in Vallecano and then we go to Qatar, so it would be nice to go for the top eight and have some rest at some point."
Bellingham was joined on the scoresheet by Kylian Mbappe and Vinicius Jr. but he isn't concerned about who scores the goals as long as Real win matches.
He said: "I don't think anyone inside the club is really that bothered about it. But I understand from outside there's an expectation of success from the three of us and from the whole team.
"It is nice that you've mentioned that we've scored, but it's really useless if we don't win games and do the fundamentals really well."