Speaking to BBC Scotland, Rennie said: "We carried a little bit high, our ball was too slow and it allowed Treviso to reorganise their defence.
"Treviso have been going really well and what history tells us is that they concede points but they hang in there and are difficult to deal with. It was an arm wrestle tonight but we got home in the end."
Rennie felt his team struggled to replicate the level of performance they delivered in last weekend's impressive win over Munster at Scotstoun.
"We didn't have quite the same edge as last week. We gave away too many soft penalties late in the game which gave them field position and they were good enough to score off a couple of them," said Rennie.
"They showed a lot of character, a lot of fight to hang in there. We expected that.
"Deep down we're pretty happy to get five points tonight and we head off to Africa on Sunday."
Having consolidated top spot in Conference A, Warriors now head to South Africa where they will face Toyota Cheetahs in Bloemfontein on Friday night.
"They're a different beast at home," he said. "The two teams that they sent away certainly weren't anywhere near their best sides when they played at Ulster and Munster. They're trying to juggle playing Currie Cup as well as playing in PRO14.
"At home they've been able to put a stronger side on the field. They've got a very dominant pack, they scrum well, have an excellent line-out drive and some absolute gas out wide.
"We're looking forward to it. We'll get a whole week together and a chance to get a little bit tighter."