Second-half goals from Lucas Akins and Marcus Haber saw Boro end a three-game losing run, coming from behind to win 2-1 after Chuks Aneke had put the hosts ahead.
Smith said: "I don't think we have been playing that badly to deserve some of the results that have come our way and we had been getting despondent, so the win is massive for us.
"We made a change and went two up top and we got more energy out of the players. There was some terrific performances and we thoroughly deserved the three points.
"We'd got into the final third two or three occasions and not found the right pass, but when we got the first goal it gave everyone the lift that we needed.
"Crewe have got a fantastic home record and it was never going to be an easy task but it was probably the most complete display that we have seen from the group in a long, long while."