Sunderland beat Manchester United 2-1 at the Stadium of Light yesterday.
The Black Cats scored the winner in the 82nd minute through Lamine Kone, but Allardyce was concerned at the time his defender headed home.
Sunderland have found wins hard to come by this season and although they largely dominated the second half against United, Allardyce did not feel comfortable until the final whistle went.
"In the second half we really took the game to them and put them on the back foot – a chance was cleared off the line, one came for N’Doye and de Gea saved – so I was thinking 'please lads, don’t throw this away', but we showed the importance of set pieces and the quality of the ball in," he said.
“Lamine sticks his head on it and it was well deserved for us because I don’t think anyone can complain that we deserved anything other than a win from the game today.”
Sunderland had 21 shots against United on Saturday, as they claimed their first league victory over the Red Devils at the Stadium of Light.
They were good value for the three points, as they put in one of their finest performances of the season.
In truth the winning margin could have been more, as both Jermain Defoe and Dame N’Doye had great opportunities to score, but were denied by David de Gea.
Sunderland’s win over United has moved them to within a point of safety, with their next match coming against West Ham United in two weekends’ time.