Aitor Karanka was upbeat despite Middlesbrough's failure to score in the draw with Everton
Leighton Baines cleared a Ben Gibson header off the line from a corner as Boro dominated in the second half.
And Everton keeper Joel Robles made a brilliant save late on, palming a fierce header from Rudy Gestede over the bar.
But Boro boss Aitor Karanka refused to be downcast, saying: “I think it was a good performance once again against one of the best teams in the league – they arrived in good form and we were at least as good as them.
Ademola Lookman firing an effort at Victor Valdes at the Riverside
“We were really organised, we had chances and we were confident.”
At the other end Victor Valdes made three crucial saves to keep Boro’s hopes of a first win in eight league games alive – stopping a Romelu Lukaku shot in the first half and twice denying Ademola Lookman in the second.
And Everton boss Ronald Koeman bemoaned Lukaku’s inability to equal his club’s Premier League goalscoring record.
Romelu Lukaku failed to equal Duncan Ferguson's record of 60 in the 0-0 draw
Lukaku’s four-goal haul against Bournemouth last week moved him within one more of matching Duncan Ferguson’s mark of 60 but he missed a glorious chance when he shot straight at Valdes.
Koeman said: “It was difficult for him because he will always get his chance and he had a big one.
“But you are not going to score 100 goals out of 100 chances. He was working hard and he got his chance to score but I think the goalkeeper did well.
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“It’s OK, it’s a clean sheet and a point – not bad. It’s our fourth clean sheet out of six games.”