The Giant Elephants had failed to win any of their last three games and were hoping for victory over Stanley Eguma's side to improve their position on the log.
With Nafiu Kabuga's second-half hat-trick handing the hosts a 3-0 win in Bauchi, the midfielder is delighted and he feels they have what it takes to challenge the big teams this season.
"I'm very happy with our big win against Rivers United because we needed to bounce back to winning ways again," Alegbe told Goal.
"We've been struggling in our recent matches and under pressure too. For that, we needed to prove our doubters wrong. It was just important that we made a statement during the match.
“Though it was not easy as many thought with the scoreline in our favour, I must admit that Rivers [United] really caused us a lot of troubles during the match.
"But we were solid and organised to get those quick goals early in the second half. That’s because we were fully aware of their plans to pull another upset like what they did at Kwara United."
"I think that the result will show everyone that we are not as bad as they think. We have good players and will need to time to blend in order to do well this season,” he continued.
“The result will revive our winning form and raise our mentality and confidence level ahead of our coming games before the mid-season break.
“With our performance on Sunday, I feel we have what it takes to compete against top teams in Nigeria (topflight) league, even finish among the top four teams."