Callum Wilson gave Howe's side the lead with a second-half penalty, but Pukki equalised with 11 minutes left on the clock. Newcastle remain winless and bottom of the Premier League. The club is six points adrift of safety following Leeds United’s win over Crystal Palace.
"It was the start we didn’t want,” said Howe.
“I really felt for Ryan (Fraser) – it was a sub we felt we had to do. I thought the crowd would get us over the line. I felt the players showed real resilience, which we’re going to need for the upcoming matches.”
Asked about Clark's dismissal, Howe said: “I think, in the cold light of day, Ciaran would have probably taken a different decision. But I think, in that moment, probably an impulse has just made him stop the striker. It probably is a red card.
"These things happen in the game. My immediate reaction was not to focus on that. It was to figure out very quickly what we had to do and find a solution to the problem.
"The last thing I wanted to do was take Ryan Fraser off the pitch. But I felt I needed to do that for the team. Feddy (Fernandez) came in, and I thought he was absolutely magnificent tonight.”
Howe went on: "I thought the players put in a magnificent performance in that respect. If we can do that 11 against 11, we’re definitely going to win some matches.
"When (the equaliser) did come, I was surprised. It was a crushing blow in that moment. The good thing was that we didn’t go under. It could be a precious point.”
The game was Howe’s first in the dugout at St James’s Park as United head coach.
"The whole day in terms of what the fans gave to the team and to me – I loved every second of that," said Howe.
“I’m desperate to reward them with the wins everyone wants."