The Teesiders are four points behind Cardiff outside the top six after their goalless draw with Doncaster Rovers, but Mowbray believes that his side can still play Premier League football next season.
"We'll keep pushing until the final day. There's a four-point gap, two games to go, so we've got to win two football matches," said Mowbray.
"That's easier said than done as the next game is at home against a team that could clinch promotion that day, so let's wait and see."
Middlesbrough last played in English football's top tier back in 2009 before relegation to the Championship.