United won their first major trophy under manager Jose Mourinho following last week's 3-2 victory over Southampton at Wembley.
Valencia and his team-mates are dreaming big thanks to the renewed confidence instilled by Mourinho after struggling under Louis van Gaal and David Moyes.
"This is the mentality that we have – that trophy has given us much confidence," Valencia said. "We are thinking about these three trophies. I think we can do it. We have to realise we are Manchester United and that we can go on to win these three trophies.
"We haven't given up hope this year [of winning the title]. We'll still fight for the league this season but if we can't do it this year then we go into next season and we will fight for the league.
"I think it's the same atmosphere [now to when Alex Ferguson was in charge]. We have that security of playing under a top manager. It's something you can definitely say. They each have their own individual style but both of them are obviously fantastic managers.
"I think a lot has changed. The atmosphere – we play with more confidence, with more happiness and with more responsibility. When you bring in new players, top-quality players, that changes the atmosphere of the team. I think we're a lot happier. We still have that responsibility on our shoulders, but you could say a lot has changed.
"I think the fear factor we have to create ourselves, we have to put the fear into teams every time they come to Old Trafford. They have to feel the pressure, that we are playing well, doing things well, playing with responsibility and we are pressing them."
United - unbeaten in 16 league matches - play host to Bournemouth at Old Trafford on Saturday.