Brennan Johnson scored twice for the visitors before Omari Hutchinson pulled a goal back in a breathless first half full of chances for both sides.
Luke Woolfenden had a headed equaliser chalked off for offside in the second period before Djed Spence and Dejan Kulusevski goals killed the game off.
Wolves' 1-0 win at Bournemouth means the Blues are now five points of safety, with a significantly worse goal difference, heading into their final 12 matches - the next of which is a Wednesday night trip to Manchester United.
Asked if he still believed, McKenna replied: "No doubt. We always will while it's possible.
"Look, it is what it is. They (Wolves) have picked up a good result today when the opposition (Bournemouth) have had an early red card after VAR. These are really, really small margins in football and they haven't gone our way in football this year.
"Of course everyone probably thinks that! But I don't think anyone can say that we've had any fortune or margins go our way too often.
"So yeah, it is what it is. We've got a big challenge to stay in the division. We know we're going to have to pick up points at a greater rate in our last 12 games and I believe that we can pick our points up at a greater rate, for sure.
"I know it's frustrating to say, but it's just the reality of the situation that we're still in a period of improvement. We've got a couple of players making their home debuts today and that's been the case almost right through the season. We've not been able to settle on relationships and partnerships on the pitch too often.
"We've got to hope for better margins and luck during the run-in, keep doing good work and push for improvement and turning margins our way.
"I believe we can pick up a good amount of points in the last 12 games. Of course it's not in our hands. If other teams win all their games then we can't control that. We can only do what we can do and that starts on Wednesday night. We've go to pick ourselves up and go again. It's another good game to try and really take on."
Reflecting on today's defeat, he said: "We're, of course, really frustrated by the result.
"I think there were lots of good things in the performance, no doubt. We started really, really well and should have been ahead.
"I think we were the better team in the first half. That's a couple of home games in a row that we should go in with a lead on the balance of play and the chances, but we go in with in with a deficit. So we're frustrated by that.
"There's no doubt that their execution, when they got their big moments around our penalty box, was better than our execution whenever we got our big moments around their penalty box. That was the difference between the two teams.
"I think there were so many good things about the performance though. There's so much growth on the pitch and a lot of growth still to come, but of course it's a stage of the season where we'd like to have the points on the board.
"It's a frustrating game, but it is what it is. We can't feel sorry for ourselves. I know we have improved in many aspects - we've had a difficult loss, so it doesn't feel like that - but I believe very, very strongly in how we're working day-to-day.
"It's clear that margins have gone against us too often. We certainly have anything that resembles luck in many different aspects this year, but also our execution compared to the opposition's execution hasn't been at the level enough.
"It's not a stage of the season where we want to talk about growth or pride in performances because we want the points on the board, but at the same time we can't lose patience with the good things that are going on. I know that they are there - there's evidence of it on the pitch and I see it day-to-day. We just have to keep working and see where it takes us."
Tottenham's opening two goals were carbon copies, with Son Heung-min getting in behind Ben Godfrey to cross for Johnson to score. Godfrey, who had replaced the suspended Axel Tuanzebe in the side, was subbed at the break.
"It's two situations where we should do better, no doubt, both in defending the individual actions and the covering of those actions," said McKenna.
"Again, you talk about margins going our way. We've got our right-back missing today for two yellows after making one foul in the first half of a game (at Aston Villa). That means we play 50 plus extra-time last weekend with 10 men and have to make another change to our backline today which, in our position, make it even more difficult.
"That was the challenge coming into the game and we didn't defend those situations well enough in the first half."
With thousands of Town fans staying until the end to voice their backing of the team, McKenna added: "The support's really appreciated and we don't take it for granted. Not every club gets it.
"I also know the supporters know the journey the club's been on. You can bored of saying it, but that's the reality. Playing Tottenham at home is a big step. Five years ago we were in the middle of League One and they were in the Champions League Final. It's been a really quick rise to this point which make sit a challenge.
"I think the supporters are clever enough here, and honest enough and balanced enough to see a lot of good things on the pitch today. There are a lot of things to take pride in in terms of how we went about it and the level of so many individual performances from young players.
"There are lots of different ways we can lose to Tottenham Hotspur as Ipswich that would still have the same outcome, but I think the supporters have taken pride in some of the things that they are seeing.
"They're frustrated, like we're frustrated, but we can work any harder. We've just got to keep working as hard as we can and as smart as we can to keep getting better. We've got to keep earning that support."