The Teessiders came into the contest off the back of a 4-1 loss at Sheffield United which had dented their play-off hopes.
The Lions are three points off the play-offs and extended their unbeaten run to seven in the Championship.
Millwall had chances to win the game but could not convert and have now racked up seven clean sheets in their last 10 matches, as well as four in a row.
Wilder said: “I asked the question to the players [if they could respond from the 4-1 defeat against Sheffield United], and they had to answer it at possibly the toughest of places, where they do ask the question all over – behind the dugout, in the stands and on the pitch.
“They’re on a fabulous run and they are a really competitive side. If you’re weak mentally or physically, they will run all over the top of you, and we weren’t. Some great challenges. I really enjoy coming here because it’s a real test of what you’re about as a professional.
“You’ve got to tackle and we did. Gary [Rowett] will look at a couple of their chances. We’re a bit disappointed with the chances we gave away.
“I can be a little bit critical of us in the final third. Didn’t really play quick enough, looking back at it a draw was a fair result. I know there was a lot of tackles going in but both teams were at it.
“We came here on quite a pivotal day for us. One point out of 15 away from home is not great. If you can’t win, don’t get beat and we take a point away from a really tough place to come.
“There was some tackles flying in and I’m all over that, I want my team to be competitive. We have to accept that if we are going to make contact with teams, teams are going to make contact with us. Get on with it and it’s a great experience for some of the younger players.
“It tests you mentally, it tests you physically and I enjoy that. I’m glad Gary is going well and I’ve got a lot of respect for Millwall.
“They’re going great at the moment, it’s always a tough place to come and especially when it’s a full house. You’re coming into the business end of the season, they’re doing well, we’re in the mix.
“There’s no hiding places here, you get tested and the older players were great. Around the final third we should’ve been better. But I’ve got to say I would’ve taken that performance and result when we walked into the ground.
“Their front three are really good – Bennett, Afobe and Jed Wallace, who I’ve known for a long time, he’s a fabulous player. They are bang in form – five wins and two draws in their last seven. That’s promotion form. We’ve come to a promotion form team and got a result, so we’ll take that.”
There was a PA announcement to tell fans to stop throwing objects on the pitch – warning that the referee would take both teams off if it continued to happen.
Wilder said: “The physio got struck by something. I’ve got to say, I was too busy to really say, but I think there was a situation with the police, where our physio wanted to give a statement.
“I was too engrossed in the game because it was that type of game, you couldn’t really take your eye off it. I think he’s okay.”
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