Goals from Erik Lamela and Harry Kane were enough to send Spurs into the quarter-finals, but Hyypia was pleased with how his players competed at White Hart Lane.
"I couldn't ask for more from the players," the Brighton boss told reporters. "We knew it would be difficult. Tottenham are good team with a lot of good players, even when they make changes.
"We thought we'd be on the defensive side and I'm very happy with the work-rate and effort. Maybe we could have played better through Tottenham's pressing, which was constant, but overall I'm pleased."
Brighton return to action in the Championship against Bournemouth on Saturday.