Spurs suffered a first defeat at Tottenham Hotspur Stadium on Saturday, with Michail Antonio's 67th-minute effort proving decisive.
Substitute Vincent Janssen had a header cleared off the in injury time, but Tottenham will now head into their semi-final against Ajax on the back of a frustrating result that also opened up the top-four race.
However, Pochettino, who in his pre-match news conference suggested Ajax may have an unfair advantage due to a round of Eredivisie fixtures being delayed, insisted that a lack of focus was not to blame for the defeat, instead saying tiredness was the determining factor.
"I cannot say we were thinking about Tuesday," Pochettino claimed.
"When the stress and fatigue arrived that is our reality. We are a very competitive team when we are with full energy, we are so focused.
"The stress and the fatigue arrived, we are competing with circumstances that are not the best. Nothing to say, the effort is there and is fantastic, but I'm disappointed with the result, because that result wasn't in our plan, but that is football.
"I think the feeling for everyone changes quickly. After our defeat today it's like we arrive in a complete opposite way. I think we knew very well to compete in the top four and the Champions League is very tough.
"We tried to win the game. We deserved it in the first half, in the second half they deserved it and that happens in football.
"It's a little bit unfair in the way that we arrive in the competition but we need to accept that. What can we do? There is nothing, only to accept that and be strong."
What it means pic.twitter.com/NqTvxSOcPH— West Ham United (@WestHamUtd) April 27, 2019
West Ham ended a four-match winless run to move themselves to within two points of 10th-placed Leicester City, and Manuel Pellegrini praised a complete performance from his side.
"I think we were a complete team, defending together without the ball, and we were playing to win," he told reporters.
"I feel that we played a big game because we defended well, because we attacked well, because we played in a way I always say this team needs to play, as a big team to go to every stadium and try to win the game.
"That was what we did today, and especially for the fans we know Tottenham is our major rival, so the fans must be very happy."