The Baggies took the lead through their first meaningful attack at the Riverside Stadium, as James Morrison found a way through from range just six minutes in.
Alvaro Negredo levelled from the spot soon after for his seventh goal of the season, however, and Boro looked the more likely to win the game from that point on.
West Brom did hit the bar three times in quick succession, though, with Matt Phillips, Craig Dawson and Solomon Rondon all coming close, and Karanka insists that he has no real complaints with the final scoreline.
"I think it was a good point. We had chances to score and have conceded a goal in a way we knew," he is quoted as saying by BBC Sport. "It is frustrating, but West Brom are a strong team and we played with everything.
"I am proud of the players. As a coach, they have done everything. The reaction was good. We had the game under control against a strong team. A point is fair for everybody.
"The opponent have a lot of experience and good players. Sometimes you can't stop them. But everybody has been brilliant. We need to forget the league position. We know we have many more games to play."