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I've been very interested in playing the Cochrane Gambit since reading about it a while back, but have had very little chance since I rarely encounter the Petrov. Finally, I got to have a go at it with good results and a very fun tactical game.
Good game. However your opponent played a poor move, 5...Be6, which is not an acceptable defense or a main line. White can play d5 immediately even.
Acceptable defenses include 5...c5 (probably the most effective), 5...Be7, 5...g6, and 5...Qe8 (the subject of a Chess Informator article).
Placing the rook at f8 was recommended in certain positions by GM Janjgava in The Petroff and GM Yusupov in The Petroff Defense. The idea is to that Black having counterplay on the f file, while placing the king safely on g8 is at least as important as contesting the e file.