And he was impressed by the hunger of players to turn the game around after trailing at half-time, admitting individuals could be rewarded with more first-team action.
He said: "Hopefully a few players have staked their claim for a regular start after Saturday's win. There are players on the fringes of the team and they are hungry to get involved.
"I want to be involved again next weekend and everyone needs to play for those places. It will push the side on."
Abbott also paid tribute to new signing Richard de Carpentier, who made his debut in Saturday's encounter.
He continued: "Richard will be an asset to the club. He's young and he's keen. He showed what he could do to get a contract and he's improved again today. He's a real talent.
"There is more competition again now. It's another player to add into the mix and that's what we need.
"Players are pushing for starts and no one's place should be safe. So players will look forward to the extra competition.
"From a personal point of view, it's great to be back and it was great to score the try. I'm feeling good and I just want to get my head down and kick on."
Warriors are the early pacesetters in Pool 2 of the LV= Cup, ahead of Cardiff Blues, who recorded an opening weekend victory over London Wasps.
And Richard Hill's men will travel to Wasps on Sunday, hoping to build on their impressive start in the competition.
Abbott added: "We take the LV= Cup very seriously and we'll be hoping to win against Wasps next weekend. We lost there in the league a few weeks ago so it will be another tough match for us."
"We need to start well and put ourselves in a position to win the game."