Louis van Gaal believes Manchester United have a great chance of securing Champions League football after coming through a “test of survival” at rivals Manchester City.

Thursday’s Europa League exit to Liverpool means only a top-four finish will do if United are to return to European football’s top table.

Van Gaal admitted in the build-up to Sunday’s match that defeat would all but extinguish their Champions League hopes, but his side produced a manful display to close the gap on misfiring City.

Marcus Rashford’s first-half strike at the Etihad Stadium saw his first Manchester derby end in a 1-0 win, making his manager believe a top-four finish is within their grasp.

“I have said in advance that we must win this game and we have done it, so I am very happy because otherwise the gap was too big if they won,” Van Gaal said.

“Or a draw is still four points, eight matches to go, so then it should be very difficult.

“Now it is in our own hands, I think. We have to win our games, we have more home matches than away matches. We don’t lose so much at Old Trafford so we have a big chance.”

Van Gaal says that the belief was palpable in the dressing room after a match which left him proud given Thursday’s Europa League exertions.

“I think that we have played a fantastic first half,” he said.

“We started the second half again very good and had the first chances — after that it was a test of survival because we were very tired.

“We have to recover within two days — that is nearly not possible and especially not when you play a game against Liverpool like we have done.

“We have and have given everything to beat Liverpool and then you have to play City.

“You have seen, for example, their result at Southampton — half-time 0-2, final time 3-2.

“I have not seen the match but I can only conclude that it is because of the tiredness. That is what we have done to them.

“My players have fought to the end with cramp — Marcus Rashford could still run with cramp. I have never seen that!”

Van Gaal’s comments came in response to a question about United targeting City’s injury-hit defence.

While coy when asked about that in the press conference, he was far more forthcoming in the broadcast interviews, especially on City centre-back Martin Demichelis.

“Rashford is very quick and Demichelis looked like the years are catching up with him,” he said.

“He was a very good defender, he was my centre-back in Bayern but that is the life of football.”

Demichelis had a torrid afternoon at the Etihad Stadium, not only being embarrassed by Rashford but providing the woeful backpass that led Joe Hart to sustain a calf injury.

City boss Manuel Pellegrini rejected the suggestion that Rashford was too good for Demichelis, although accepted his substitution early in the second half was a result of a bad day at the office.

“He was nervous,” Pellegrini said, having taken him off in the 53rd minute. “He was not having a good day.”

Pellegrini, who walked out of his TV interview, struck an understandably frustrated figure in the post-match press conference, having seen City’s title hopes extinguished as United moved to within a point of them in fourth.

The Champions League quarter-finals may await the Capital One Cup winners, but they have now only won one of six league matches, raising questions of whether Pep Guardiola’s impending arrival has negatively impacted the squad.

“I don’t think that I lose any control,” Pellegrini said. “If you see the attitude of the team today, it reflects that we are involved in what we want to do.

“Of course it is not the best way to finish the season and maybe one thing is linked with the other one, but I repeat I am happy with the attitude.

“The players are focused in this season and want to finish as near the top of the table as we can.”