Lyall netted a late penalty to put the icing on the cake for David McCallum’s side in the 4-1 win at rain soaked Cappielow.
Ross McCausland’s brilliant opener was cancelled out by Bradley Rodden, before Findlay Curtis scored and then set up fellow sub James Graham, with Lyall completing the win over the League One outfit.
The midfielder was delighted to keep their SPFL Trust Trophy campaign going as well as how the youngsters dealt with the Wasps’ physicality.
He said: “We started the first 20 minutes really well but we slacked off and they grew into the game and got their goal.
“In the second half we were a lot better and started playing the way we know we can and got three late goals.
“We knew if we kept going the goals would come and we know we are a fit team and if we kept going we would get chances and we took them.
“It is brilliant the impact the subs had as some of the boys can’t play the full 90 minutes and you need boys to come off the bench.
“It was some of the younger ones’ first taste of playing against men and they were brilliant.
“It is different to what we are used to as we are used to technical games.
“But you need to develop the physical side of the game and play against Alloa who are a physical side.
“Once we coped with their threat we dealt with the ball well and that showed in the end with the four goals.”
The victory secured a fourth round tie with Championship side Airdrie and with Monaco coming to Ibrox next Saturday, Lyall reckons exciting times are ahead for the squad.
He added: “It is brilliant to have these games coming up against Monaco and then Airdrie in the next round of the cup.
“They are a league above Alloa and it is two big tests, but hopefully we can put in similar type performances and get another two wins.”