The Bolton boss was pleased to see the on-loan Diouf get on the scoresheet during yesterday's draw with West Bromwich Albion - his first since his infamous ban for spitting a month ago.
Allardyce feels that the African forward must calm his temper when dealing with the large number of challenges which come his way from over-eager opposition.
"There was a certain composure, certain calmness in his play. I don't want to speak too soon, though, as I don't want to tempt fate.
"He gets a lot of challenges against him because of the way he plays. He likes to retain the ball. He has got to resist the temptation to react against those and keep playing the game. There can be nothing better for him than scoring a goal like that."
Vaz-Te on the other hand, could have forced his way into the line up for the midweek game with Birmingham City following a number of cameo roles from the substitutes bench.
The Portuguese teenager could replace the injured Kevin Davies during the match at St Andrews having impressed the Bolton staff during his spell in the first team.
Allardyce feels that the 18-year old showed enough on his one and only Premiership start at Manchester United to be considered for the game against the Blues.
"Ricardo has tremendous skill and pace and, above all else, he his playing with no fear."
"He is a young man and I am pleased to have him in the first team squad. The squad is fearful and nervous at the moment and it is good to have a player coming in who is very positive and is eager to make an impression.The lad is a breath of fresh air and I hope he can keep it up.
"I gave him a chance to start the game at Old Trafford on Boxing Day and he did nothing wrong. He has a very good chance of starting the game at St Andrew's on Tuesday."