The game ended 1-1, with Tim Cahill’s header cancelling out Phil Bardsley’s stunning opener, although Everton dominated in the second half.
And Round believes his team could have had “a penalty or two” and admits they are disappointed not to win the match.
“We’re very disappointed from the second-half having not gone on and won the game,” he told reporters.
“We had enough dominance and enough opportunities. On another day maybe we’d get a penalty or two, but we are disappointed to go in [the dressing room] having only drawn.”
Everton felt aggrieved at referee Andre Marriner’s decision not to award them a penalty and Round thinks the Toffees were on the wrong end of two controversial decisions.
He continued: “I think there’s one [penalty] for definite on [Royston] Drenthe in the first few minutes, it seems very strange why that wasn’t given.
"The second one [handball by John O’Shea], we think it’s a penalty, they would say it isn’t. It’s one of those you either get or you don’t.”
The 41-year-old did admit that there was a foul in the build-up to Everton’s equaliser but praised both goal-scorers.
He said: “Tim [Cahill] was terrific today. I thought he looked fresh and full of energy. He was a threat in both boxes and deserved his goal.
“[Their goal] was an excellent strike. They are quite dangerous from set-plays so we set up early but he’s [Jack Colback] cut it back and he’s [Bardsley] hit a wonderful strike.”
Round also admitted it will be more difficult for Everton to progress now that they must travel to the Stadium of Light.
He added: “They’ll start as favourites at home, obviously, but Everton have a knack of upsetting the odds sometimes.
"Last season we drew at home against Chelsea, and went away [to Stamford Bridge] and won, so it’s within our capabilities, that’s for sure.”
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