United remain on course for a return to Champions League football next season and have a realistic chance of collecting some silverware after reaching the fifth round of the FA Cup.
But the former Netherlands, Barcelona and Bayern Munich coach admits he still has a lot of work to do to restore United to their former glory.
The United boss said: “I am only satisfied at the end of the season – to be third and in the next round doesn’t count now.
“We are on our way but we have to play a lot of matches still and there are still three to go to the final. That is our goal. We have to wait and see if we reach that goal.”
United have lost just once in their last 16 games in all competitions and travel to West Ham on Super Sunday off the back of convincing wins over Leicester and Cambridge in the past week.
But the 63-year-old is under no illusions about how difficult the visit to Upton Park will be, with West Ham enjoying a solid a Premier League campaign so far.
He said: “I said at the beginning of the week, before the game against Leicester, that this shall be an important week, that we had to win all the three matches.
“We beat Leicester to go third, after that we beat Cambridge, so we are in the next round of the FA Cup. Now we have to continue. All the players know that is true.
“But it is not so easy. We have to play away against West Ham. It was a tough game in Manchester. It shall not be easy but we want to continue and if we want that we have to win in London.”
United struggled in the early part of the season, but despite a marked improvement in recent months Van Gaal insists United can still get much better
He said: “Okay, until now we could have played better in ball possession – we have had unnecessary losses in ball possession and we have to improve that.
“But I think we have a very good defensive organisation and also a very good attacking organisation. We are fourth in the scoring goals league and also third or fourth in the defensive way of playing.
“I don’t think we are very bad – we are very good – but we can improve. We have to improve a lot in my opinion, but at the end maybe we can see we are the best team.”