While United are only considered an outside chance of winning the Champions League, Young believes they are capable.
"Of course [we can win the Champions League]," he said.
"You don't enter a competition not to win it. That's what we will be looking to do and take each game as it comes.
"The next one is against Sevilla. That's a tough away game like Huddersfield, like Newcastle away. That's what the stadium is like. We just have to concentrate on ourselves."
A brace from Romelu Lukaku helped United past Huddersfield and into the FA Cup quarter-finals.
The Belgium international has scored 21 goals in all competitions in his first season at Old Trafford and Young hailed the 24-year-old.
"When you have a striker scoring goals, it's always important. His hold-up play, his all-round game was fantastic at Huddersfield, and he's done that all throughout the season," Young said.
"He's getting goals. When you've got someone who can hold up the ball like he can and get in the box it's fantastic.
"And you can see the combinations between them. Alexis [Sanchez] comes inside and Rom's seen him and picked him up as well and they're picking each other out and they have worked well together so far."