Handed the reins the previous day following the exit of Darren Moore to Sheffield Wednesday, Butler, 37, watched his side secure their first win in six League One matches.
A goal from Reece James - his seventh off the season - put the hosts ahead and a blistering strike from Fejiri Okenabirhie - his 12th of the campaign - midway through the second half added to Rovers tally.
A late consolation in stoppage time afforded hope to Pompey, in the top-six picture with Rovers and they were denied a point by a brilliant last-ditch challenge from James to prevent a leveller.
Butler said: "It has got to rank alongside my debut if I am totally honest. I took charge of the FC United and Wolverhampton games (with Moore and his coaching staff self-isolating), but to take charge of the professional team (as permanent manager) and the (Doncaster) Belles is a huge moment for me.
"It ranks pretty much up there in football terms of moments I will never forget.
"I was in the dressing room before the match and I said to the players that I wanted a performance full of desire, commitment and hard work and when we had the ball - express yourselves.
"To a player, I thought they were excellent. The players who started were excellent and were those who came on who made an impact. It was a positive result.
On two excellent goals from James and Okenabirhie, he added: "The goal was something Reece works on well and he has got a lot of goals this season now and it was a great ball from John (Bostock) to spot the run and we knew we could get in between their backline and the goalkeeper and it was something we worked and with Fay (Okenabirhie) - what a finish. You ask players to come on and make an impact and what an impact.
"What a tackle from Reece as well at the end. If we had come in and drawn 2-2, it would have felt like a defeat and if you can see the reaction of the players as well afterwards, it was incredible.
"You could just see the camaraderie in the dressing room after. Even the substitutes were all buzzing for the lads because we won the game and that is what I want to bring to this club, a winning mentality and not just the 11, but the whole team."
The only downside saw John Taylor hobble off with injury in the first half and he will be assessed.
Butler added: "It was unfortunate that Tayls was injured and we will have to get that assessed. But what I said to the players is that it is a squad game and if you are performing, you will get a shirt and the lads that did not play in their game were out there training on the pitch (after) to get their match sharpness. It is a whole squad game and everyone will be needed.
And on his decision to hand young keeper Louis Jones a league debut at the expense of loanee Ellery Balcombe, he said: "It is a decision I made. I spoke to Ellery about it. Ellery wants to play every game, but at the same time, Louis has deserved his chance.
"It was my first game in (full) charge, so you live and die by the sword and I made the decision and I thought Louis was excellent. I am really pleased and I have two really good keepers pushing each other and that is what I want. People pushing each other.