United bowed out of Europe on Wednesday evening, going down 3-1 to Bayern Munich in the Allianz Arena, which gave the reigning European champions a 4-2 aggregate win.
The result means that, for the first time since 1995, United are highly unlikely to be present at Europe's top table next season.
After the defeat in Munich, Moyes told Sky Sports: "We have not got Champions League football, that's the way it looks, but I believe that it is not far away, and hopefully it will be one year away.
"We have got to rebuild and our focus is to get a team that can get back into this competition. It is a great competition - we have really enjoyed it - and there is no shame in going out to Bayern Munich."
Moyes was asked whether he believed his job might be in some doubt, after his failure to get into the Champions League.
"That is not a question for me, as my job is just to get on and do the job," he insisted.
"I have found everyone at the club very good, and my focus is to get a side that gets us back in the Champions League and that is the main objective."
Moyes insists that the club's hierarchy are backing him and plans to rebuild the side are already in motion. He insists not being in the Champions League will not hamper their pursuit of any of their top targets.
"The club have never had any problems, on anything we have talked about" added Moyes. "The club are looking to spend the right money on the right players that are available. It has nothing to do with Champions League football.
"Any players that we have sort of quietly discussed with, I think they are more than happy to join Manchester United.
"The ones who quietly, someone might have had a word in their ear, have all been keen to come as it is a short thing and not a long thing and they are all very keen to join such a great club."
Turning to the game, and Moyes felt his side were unlucky, having actually taken the lead in the Allianz Arena through Patrice Evra's 57th-minute strike.
But United could not defend their lead, as Mario Mandzukic levelled just seconds after the re-start, before Thomas Muller and Arjen Robben settled the tie.
"When you're a schoolboy, you get told to make sure that when you score, you don't concede straight away. We conceded too quickly," he admitted.
"It was always going to be a tough night and once we got the first goal, we had to give ourselves five or 10 minutes where we could stop them getting the ball but from the kick-off, they went up the pitch and scored.
"I don't know whether it was a bit of concentration, thrilled we got the goal but we have got enough experience on the pitch where we should have done it - but they didn't do an awful lot wrong tonight, I thought the players played ever so well, and I was pleased with the performance and just a couple of small errors that cost us in the end.
"I never thought we were out of the game, I always thought we were in with a chance and at 2-1, we needed just to get that goal to get back to 2-2, but that third goal killed us. That didn't go for us, and I thought that was a bit of bad luck.
"They are a really good side and they showed it, but I thought we did what we had to do tonight - I thought we came here and made it difficult for them. Tactically we tried to stifle them as much as possible but if you lose a goal just after we score, it makes things really difficult."