Rhodes, 26, came on as a substitute to draw Boro level in the 93rd minute of Tuesday's 1-1 draw at MK Dons.
That draw took the Teessiders to the top of the Championship, a point clear of second-placed Hull City.
"When a player goes to a team not winning, everyone expects two or three goals every game," said Karanka.
The Spaniard told BBC Tees: "It's really difficult for him and it's good for him to take the pressure off. I'm really pleased for the whole team because we played until the end."
Scotland international Rhodes is yet to start for Karanka's side despite his arrival, and despite Boro's four-game winless run.
"I thought it was the best option [to keep him on the bench]," Karanka added. "I didn't want to make a lot of changes, I wanted to keep the nucleus of the team."
Jordan Rhodes' first goal for Middlesbrough has "taken the pressure off" after his £9m move from Blackburn, said head coach Aitor Karanka.