Everton recorded their biggest win of the season and consolidated sixth place in Premier League with a 4-0 defeat of Wigan at Goodison Park. On loan striker Jo scored twice, once in each half, whilst Marouane Fellaini and Leon Osman completed the rout against a disappointing Latics outfit.
He told Sky Sports: "Certainly, (it was a hugely satisfying afternoon), especially after international week.
"We performed really well. I thought our general football was very good.
"I have always said that if we can try and look to the UEFA Champions League we would try and do so.
"We will keep trying. But obviously Arsenal are the side in pole position. It's a long shot. But who knows."
Moyes also reserved praise for on-loan striker Jo and midfielder Osman, with the duo shining during the triumph.
He added: "I thought Osman was probably the pick today. That was him back to his best.
"Jo has shown bits of the form he showed at CSKA Moscow. His goals are really important for us."
"Certainly defensively we found it a struggle against a very good Everton team. Our performance was very disappointing.
"I have to pay a big compliment to Everton. Sometimes you get your backsides kicked. And that certainly happened today."
"The biggest problem we had is that four of five players really struggled today having travelled all over the world for internationals.
"We had no real hunger about us today and I hope because we've reached 40 points we don't think that's job done."