Louis van Gaal’s side went behind inside the first five minutes of the match thanks to James McCarthy’s strike before goals from John Stones and Kevin Mirallas wrapped up the three points for Roberto Martinez’s side.
Man United had the large majority of possession but they could not fashion themselves any real goalscoring opportunities at Goodison Park in what was a hugely disappointing afternoon.
Smalling insisted United’s poor display meant they did not deserve to take anything away from the match.
Speaking about the game, Smalling said: “We were second best. This is a massive wake-up call for us.
“I think it was always going to go down to the final couple of games. We’ve got four big games now in which we’ve got to make sure we were better than today. I think we’ll go back and look at the video tomorrow and, come the next training session, we’ll be eager to put this right.
“We haven’t been the second-best team in games this season, even when we’ve lost, we’ve always had that aggression and those tackles but today we were far from it. I think we’ll see a different Manchester United next Saturday against West Brom.”
Smalling is absolutely right that United seemed to lack any desire against Everton. The club are still in a strong position in the race for the top four but they will need to produce much better performances in the final few games of the campaign.
He added: “I think in the last two games we’ve had good possession, and especially in the first half today I think we created some good chances, but it was a game in which you needed to take chances and, if we had, it might have been different. In terms of aggression and one-on-one battles we were off the pace.
“The goals [we conceded] were very uncharacteristic, one from a corner and one from a breakaway where everyone has their positions and knows their jobs, so there’s no way they should be getting through as easily as they did today.
“We felt that our play at times was good and we played a lot of passes in towards their box. Given how we’ve played in the last few games, teams are more defensive and today we couldn’t find the answer despite a couple of good chances in the first half.
“We kept plugging away but couldn’t find those gaps. It was difficult. We’ll make sure we learn from this, the fans deserve a lot better than what they saw today.”
Meanwhile, van Gaal will be hoping that Wayne Rooney’s injury is not too serious. The United captain hobbled off late on against Everton, which was a worrying sight for fans.