The Dutch-Romanian pairing won 7-6 (7-5) 6-4 6-4 in one hour and 52 minutes.
Murray had hoped to claim a first men's doubles Slam title having won the mixed doubles with Jelena Jankovic in 2007.
The 29-year-old was watched by younger brother Andy on Centre Court, 24 hours after his singles semi-final defeat.
"I didn't know he was coming till I heard him shouting," said Jamie Murray.
"He was shouting all the time, encouragement. It was cool.  It was nice to see him out there supporting."
The brothers must now regroup after Wimbledon disappointment as they are both part of the Great Britain squad which will take on France in next week's Davis Cup quarter-final at Queen's Club.
"It's an exciting match to look forward to," he said. "It's a big tie for us. There's going to be a lot of people coming out to support. Motivation is high for the match."
Murray and Peers had three chances to break serve in the first five games of the doubles final but could not convert, and Rojer and Tecau took advantage.
Rojer hammered away a smash to convert their third set point in the tie-break, and when Peers netted a volley to drop serve early in the second, the lead was convincing.
A Peers double fault invited huge pressure at 4-4 in the third and Rojer proved more solid than Murray at the net to earn the decisive break.
The fourth seeds served out the match to love and fell to their knees in celebration, with Tecau finally getting his hands on the trophy after three times finishing runner-up.
"It was a good tournament for us," added Murray, who had never previously been past the quarter-finals of the men's doubles in a Slam.
"We got to the final of Wimbledon, which is not so easy to do.  I mean, my best result in a Grand Slam by quite some distance, I guess.
"It's sad to lose but I guess overall it was a positive tournament."

The body of Leonne Weeks was found in Dinnington, Rotherham, on Monday at about 11:00 GMT.
An 18-year-old man is being quizzed over her murder and a woman, 26, is being held on suspicion of assisting an offender.
Her family said they were "devastated at the loss of our beautiful daughter and sister Leonne".
"She was very much loved and will be missed by all of us," they added.
For live updates and more across Yorkshire
Rebecca Staples, principal of Dinnington High School, of which Leonne was a pupil, said the community was "reeling".
"We have extra security at school at the moment because we wanted to be sure ourselves and want parents to be sure that everyone is absolutely safe," she added.
"I think there's also a feeling of underlying anger that something like this could have happened in such a close community to one of our own.
"She was a lovely student, a lively student and it's a sad loss."
A post-mortem examination took place on Wednesday and found she had suffered multiple stab wounds, South Yorkshire Police said.
Temporary Det Ch Insp Martin Tate added: "Leonne's family have had their entire lives turned upside down over the last couple of days and are utterly devastated."
Police have been granted an extension to the murder suspect's custody as they continue with inquiries.
Friends and family posted Facebook appeals for Leonne's whereabouts on Monday morning after she failed to return home.
By 18:00, comments hoping she would be found safe had changed to well wishes to the family after "heartbreaking news".
Patrols have been increased in the area to reassure the community and anyone with information is urged to make contact.
Britain's Jamie Murray and Australian John Peers missed out on a first Grand Slam doubles title together as they lost to fourth seeds Jean-Julien Rojer and Horia Tecau in the Wimbledon final.
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A 16-year-old girl found on a path had been stabbed to death, police said.