Manchester United manager Louis van Gaal said Champions League qualification was "still a rat race" after his side beat Aston Villa at Old Trafford to go third in the Premier League.
United were showing signs of becoming frustrated until Ander Herrera broke the deadlock just before the interval.
Wayne Rooney controlled, turned and shot to score an outstanding second, but a rare mistake from David De Gea moments later gave Christian Benteke a goal and Villa hope.
But Herrera struck again to put United eight points ahead of Liverpool and the BBC quoted Van Gaal as saying: "We are still not certain about Champions League qualification -- it is still a rat race.
"But we have given a blow to Liverpool, and Southampton also lost. It is a big gap. But we have to play the top three, so it is still a rat race.
"We are looking up and we have to win every week, but anything is possible. We have made a big gap to fifth, but we can suffer a defeat.
"Liverpool are now eight points behind us and we are more than eight points behind Chelsea. We probably won't be champions, but we can apply pressure.''
Van Gaal praised United for a "more controlling" second-half performance and added: "It is always difficult to win against a side battling relegation.
"We have created four or five chances and didn't give any chances away in the first half. We scored the first goal at the right time at the end of the first half.
"The first half was a good performance, but we have to finish more chances. The second half was more controlling."