Victory at the weekend pushed Lambert's side up to fourth in the Championship and condemned the Teesiders to the relegation places.
But despite their steady progress, Jackson, who by scoring the only goal of the game took his tally to four for the season, says City need to remain grounded.
"It's a great start but it's not about right now," he said.
"It's about where we are at the end of it. We have to keep maintaining consistency and keep picking up points any way we can."
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