Rovers headed into the game without a victory and with just one league goal to their credit but El-Hadji Diouf, Jason Roberts and David Dunn served up a comfortable 3-1 win.
Allardyce said: "I don't care what anybody says - the pressure really comes on you when you're still looking for your first win. But we've got what we deserved."
Allardyce singled out the recalled Diouf and the tireless midfield prompting of Dunn as the chief reason why his side managed to put their poor start to the season behind them.
Allardyce added: "The flair players like Diouf make a big difference when they use their skills in the right areas. It's the same with Dunn - his skill and talent is what we need on a weekly basis.
"It's great when you can win and entertain like that at the same time. We've put in a really good performance with the right result and one we can hopefully take a lot of confidence from."
Allardyce admitted his one slight criticism was of his team's failure to press home their advantage even more, instead handing Stefan Maierhofer a late consolation.
Allardyce added: "The only disappointing thing from my point of view is how sloppy we were on their goal. But in the end that didn't matter."
Wolves boss Mick McCarthy's disappointment at his side's defeat was increased by his decision to punish George Elokobi and Ronald Zubar for turning up late to the pre-match meeting.
Elokobi stayed on the bench all afternoon and Zubar did not figure at all, and McCarthy confirmed the pair would face further disciplinary action by the club.
McCarthy said: "They turned up late for the team meeting. If you don't turn up in time you don't play. Those two are rooming together and I'm waiting for them at twenty to one."
The Wolves boss admitted his disappointment at the way his side failed to take advantage of early openings, not least Christophe Berra who missed a simple fifth-minute chance.
McCarthy said: "I thought we started the game reasonably well and had the best chance but we gave the ball away and if you let Diouf go one-on-one it will end in tears.
"We started the second half really well and we had a chance then we didn't defend from a corner kick. If you give two goals away the end result is going to be a defeat for us.
"We kept going at 3-0 and got one back. Wayne Hennessey had a good game and he needed to. But getting beaten 3-1 I'm hardly looking for positives to brighten up my evening."