Having frustrated Middlesbrough for long stages, Eustace fancied the Rams to snatch all three points.
Instead, it was Boro who forced the late breakthrough, with Finn Azaz striking with 10 minutes to play to extend Eustace’s run of defeats to three games since he took charge of Derby.
The Championship strugglers headed for Teesside intent on frustrating Boro and Eustace was delighted with how his players executed the gameplan. Marcus Forss had a good first half chance for Boro and Azaz hit the post, but Michael Carrick’s side struggled to create any clear cut openings in the second period.
That was until Azaz finally found a way through with his 10th goal of the season.
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“I’m really disappointed to lose the game,” said Eustace.
“In the second half we weren’t troubled at all and I felt we’d go on and win the game if I’m being honest, especially in the last 10 minutes. So to concede in the way we did was really frustrating and disappointing.
“I sensed that after an hour (that Derby could win). I was very pleased with the structure, the way the team were defensively sound.
“We were up against a team with a lot of very good players. They had a couple of chances and we were under pressure but we defended well.
“In the second half we told the team to get a bit higher up the pitch, and that helped. We’re coming to a top team and the way we competed and the attitude was very good. It’s just very disappointing to concede in the manner we did.”
Derby dropped to the bottom of the Championship after their winless run stretched to 12 games, but Eustace insists the Rams have the fighting qualities required to get out of trouble.
He said: “The players are low, of course they are, they’re disappointed, but they still have to take a lot of positives from the game.
“The lads are all disappointed but what they showed from an attitude point of view is really pleasing and there’s still a lot of football to be played.
“I’ve only been here two weeks. We have to have a bit of realism. You can see the spirit and togetherness is there. It’s just the moments where we’ve let ourselves down with the quality and concentration.
“It’s just about keeping the level of concentration for the full 95 minutes. We have two home games coming up and we have to be really positive.”