Wilder was quickly installed as the leading contender with the bookmakers to replace Sean Dyche following his shock sacking.
The Boro boss has twice been asked about the speculation in recent days over the Easter weekend but he didn’t shut it down completely.
Wilder has been linked with the newly-vacant Burnley job in recent days, but he was not willing to engage in discussing that given the nature of his side’s defeat against Huddersfield on Easter Monday.
“Listen, I’m an emotional guy. We’ve just got beat from a footballing point of view. I’ve just got beat as manager of Middlesbrough, so I can’t stop any of that stuff (Burnley speculation), but I’m not so sure it’s the right time to ask anything like that after a really disappointing defeat from our point of view,” he said.
While Huddersfield keep marching on, Middlesbrough’s four-match winless run – including three straight home defeats without scoring – has seen them drop out of the play-off places.
Wilder added: “The goals that we have conceded in those three games, four terrible goals. It’s not a good time, the timing has not been great for us not to cement a place in the play-offs through three home defeats on the spin.
“It is still alive. It is going to be a struggle to hide my emotions because I’m not a very good actor. I am deeply disappointed, we fancied it today. We set it up with good performance on Easter Friday (at Bournemouth) and after half an hour I was delighted.
“I am not looking beyond today, I am analysing today, the immediate reaction. And it is one of huge disappointment.
“They came to counter-attack, sit in and it’s not an issue. We had to break them down. It gets decided in both boxes, they defended their goal fantastically well.
“We didn’t risk enough, cross it enough, shoot enough, we didn’t manage to pick anyone out from good areas. The second goal was a huge boost for them.”