Momentum may be with Sale, who moved to within one point of 11th placed London Irish with a fourth win in all competitions, but Diamond said his side were still in the mire as they battle to rescue their status, adding that no team that was bottom at Christmas has managed to stay up.
"London Welsh are a good side and we thought we had got away at half-time but they came back, scored a penalty and got their try," said the Sale rugby director. "For us, it was the fourth win on the trot and the momentum has helped us. We have remained injury-free and we have to look for survival so it was good to get those four points."
The scale of the task, though, is still clear to Diamond and it does not get easy with some of the league's big hitters aiming for points towards the play-offs.
"We are still bottom of the league as we sit here tonight and we have Harlequins and Leicester to come in the next fortnight. We have got a job on our hands and we are by no means out of the mire. We have just got to keep training and getting points because I don't think any side that has been bottom of the league at Christmas has stayed up.
"Now we have beaten Exeter by a couple of points and London Welsh by a point. If we can continue to do that in three or four games (to the end of the season), we will survive by the skin of our teeth."
Gavin Henson played a key role in the match, but London Welsh head coach Lyn Jones said there was disappointment at losing by so narrow a margin in the home dressing room.
Jones said: "I said before the game that this would go right to the wire and I firmly believe so. Today we were on the wrong end of a one pointer and the game could have gone either way.
"We didn't take our opportunities when they arose but we picked up a bonus point that takes us a step closer to Worcester (who are ninth). Before the game, we spoke about silly penalties and we were going well but then our knees buckled, Sale came back into it and then we were under pressure.
"A lot of Sale's points came from unsmart play from ourselves. It is dealing with pressure which we are not doing at the moment."
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