Everton has won four out of five games since Allardyce was appointed as the full-time replacement for Ronald Koeman at the end of last month, and Rooney has scored in three of them to take his tally for the season to 10 goals.
"That settled us down and we were nice and comfortable after that but we were never that until we got the second goal. We were too negative in the first half".
Sam Allardyce is not expecting the January transfer window to be busy at Everton, although he would like to sign an additional forward.
The latest win lifts Everton up to ninth - an awesome turnaround since the dark days of Ronald Koeman's reign.
He said: "I think the aim is the top half and not get too carried away".
"To collect 13 out of 15 points is outstanding considering the position where we have come from", said Allardyce.
'That's our 30th game this season after starting in July so the quicker we can get the squad into place, the more I can look at the market and decide how much we really need.
"And a team that comes from 1-0 down to win, like we did tonight, shows a lot of character. But the character was there today when we needed it".
The Iceland worldwide, who left the Swans in a £45million summer move, scored the vital second after Dominic Calvert-Lewin had cancelled out Leroy Fer's opener by converting Wayne Rooney's saved penalty on the stroke of half-time.
The Goodison Park fans were expecting to cheer captain Rooney, who assumed charge of penalty duties, however, the boyhood Blue saw his shot pushed to the post by Fabianski, but not beyond Calvert-Lewin, who was there to pick up the rebound and power home for the 1-1. - Rooney has failed to score with 10 of his 33 Premier League penalty kicks overall, with only Alan Shearer failing to convert more (11 of 67).
"I have not set targets for goals, but I am in good goalscoring form and hope that can continue". The more I play the better I feel.
He added: "It was a unusual feeling playing against (my former club) but it's good for us, puts us in ninth and it was an important three points after an important few weeks".
However, there was plenty of that aimed at former Swans defender Ashley Williams five minutes later when he lost Fer at a corner and the unmarked midfielder stabbed home Carroll's inswinging corner from four yards. "He wants to go out and prove he is worth every penny we paid for him".
Swansea boss Paul Clement, on the other hand, after another frustrating result, will have plenty to reflect as his team stay rooted to the bottom of the table.