Kasey McAteer’s finish strike and Jack Clarke’s late penalty saw the Blues twice come from behind to claim a point that leapfrogs them back above Millwall into second spot.
It leaves Town needing nine points from their remaining four matches to be virtually guaranteed a place back in the Premier League.
A hectic finish sees McKenna’s men now take on three away games in a week – Charlton (Weds), West Brom (Sat) and Southampton (next Tues) – before finishing with a home clash against QPR.
“Let’s enjoy it,” said the Blues boss. “I like the way we went about the game today.
“Now we know we’ve got a really tough week. Three away games in six days. We’re in a good position, but we’re no illusions that it’s going to take an incredible effort to see if we can bring it back here on the last day.
“It’s Charlton next and we know we’re going to have to stand up to it and deliver a performance.”
Reflecting on this afternoon’s draw, he said: “I thought it was a really good game. First half was the game we were hoping for. We were really dominant. It was a really top performance in most aspects against a very good team who have been dominant in pretty much every game they have played this side of Christmas. So we are really happy with the general level of that performance and to do it at this time of the year, I think, shows a lot of good things of where we are at.
“We are disappointed to not be ahead at half-time. We didn’t have much to defend in our box but didn’t defend the moment that we needed to well enough and then we weren’t clinical enough in their box on our moments or on our set plays to have a lead at half-time that I think we would have deserved.
“The start of the second half was okay, and I still thought we were the team in the ascendancy, then the game and the momentum really changed with their second goal. We were disappointed with that one and then they were excellent for the 15-20 minutes after that. We went from being really strong in the game to probably hanging in the game.
“Then of course it changed again after the second goal and we were the team really pushing to win it at the end.
“We were, in my opinion, the better team for a lot more of the game. But Middlesbrough certainly had that big spell where they showed their quality and we had to hang in. So we take the point and we go to the next game.”
Clarke chance to level from the spot late on came after Adilson Molanda grabbed at George Hirst’s waist in the box.
Boro boss Kim Hellberg wasn’t happy with the decision, but McKenna said: “I watched it on the iPad on the side of the pitch and, to me, it looked pretty clear in terms of George’s run onto the cross and Malanda pulls him from the wrong side.
“It looks pretty clear to me. It looks similar to the one Darnell (Furlong) gave away at Watford where you’re at the back post and you pull from the wrong side. It’s similar to the we should have had here against Leicester with Cedi (Cedric Kipre).
“I’ve not watched through all the different angles, but I didn’t see anything overly contentious with it on the first glance that I had.”