After announcing his retirement from worldwide football yesterday, he said: "One of my very few regrets is not to have been part of a successful England tournament side".
Rooney leaves England's team having scored and England-record 53 goals in 119 appearances.
Rooney, though, did later open the door on returning to the England set-up in some sort of future non-playing role and he is adamant that the next generation will soon deliver in a summer tournament finals.
"With the season Wayne had last season - with him not being given the chance to play as much as he would have liked - he is concentrating on his football at Everton and if England comes knocking he has more goals to go for", the Everton captain said.
Allardyce believes that Rooney's decision to quit global football is good news for Everton, as the Toffees will get some quality three to four years of service from him. I have discussed it with my family and Everton's manager.
"I think you have to select players on form and I took no pleasure from leaving Wayne out of those squads", he said.
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Southgate said he had a long conversation with Rooney, who announced his retirement on Wednesday, about his decision and had been considering including him in the squad. Now I want to focus all my energies on helping them be successful'.
A frustrated England drew 0-0 in a group match against Algeria, prompting English fans to boo their players, after a less than average performance.
Rooney, 31, announced on Wednesday that he had called time on an global career that has seen him net 53 times in 119 appearances after Gareth Southgate tried to recall him on the basis of his good form at Everton this summer. "It's a pity he will miss the next World Cup for England", Eriksson told Sky Sports News.
"Well done on a record-breaking @England career, @WayneRooney!"
Rooney had made his debut, and become England's youngest player at 17 years and 111 days, in a defeat by Australia at Upton Park in February 2003.
Wazza's last appearance for England came in November 2016 against Scotland. So many players of his stature would sulk if asked to play somewhere that they didn't consider their best position, but Wayne didn't. "If it was up to him, he would play every minute, every second!" "No-one enjoyed playing for England more than Wayne Rooney".
"I don't give him advice". But I think you've also got to respect his decision and the thinking behind that.