Boro dropped into the relegation zone as their winless run in the Premier League extended to a 10th match at the bet365 Stadium, slipping down a place to 18th, with Crystal Palace moving up to 17th and three points clear of them after a 2-0 victory at West Brom.
Karanka's men - the lowest scorers in the division, with just 19 goals - failed to hit the back of the net for a fourth successive league game, and the Spaniard was left disappointed by their defending for both Stoke goals, netted by Marko Arnautovic in the 29th and 42nd minutes.
Discontent among Boro fans at the ground could be heard, with some boos coming from the away section, while at one point there seemed to be a chant for Karanka to "go home".
Asked about that afterwards, Karanka said: "I didn't hear.
"But I came here because the chairman (Steve Gibson) called me three years ago to help the club to be in the Premier League, and I will leave the day that the chairman says.
"The only thing I can do is work harder every day."
Karanka, who got Boro promoted as Championship runners-up last term, feels there is plenty that needs addressing but emphasised the need to "just keep going".
He said: "The problem I think is a lot of things - it's not just one.
"Because if it was just one, I would fix it, but it's more than one, more than two, more than three.
"We are in the bottom three in March. For a recently promoted team to be for the first time in the bottom three in March is because we are doing something well.
"We knew we were going to be fighting until the end to survive and my thought is just to keep going."