Michael Smith gave the Pirates the lead but Jason Scotland, Tommy Smith and Aaron Cresswell responded for the hosts, who also missed a penalty through Michael Chopra.
Jewell was delighted with his side's performance and praised their recent efforts, also taking into account the pre-season friendly victories against West Ham and Colchester United.
"If the players keep showing the same hunger, effort and desire I won't be able to ask for more," he said.
"We might be lacking in certain departments and in terms of experience, but we're not lacking in endeavour.
"It's easy for heads to go down after falling behind but we didn't let that happen.
"We showed character and spirit.
"We've got players who enjoy passing the ball and playing at the tempo we want to play at and it was a very important start to the season.
"Bristol Rovers made it difficult for us and had lots of the ball.
"But we dominated the whole match, if I'm honest.
"We didn't do enough with the ball in the first half but in the second we took the game to them.
"We had some great opportunities and could have won by more."
Jewell is still hoping to add to his squad before Saturday's Championship curtain-raiser at home to Blackburn.
"It's been a really frustrating few weeks," he said.
"We've thought we've had deals tied up and then things have happened.
"What could have gone wrong, has gone wrong but we've just got to be patient."
Rovers boss Mark McGhee had no complaints after the defeat, saying: "It was a fair result.
"We were containing them and felt 'maybe' as long as it was 1-1.
"But they were always the more likely team to score.
"My lads take an awful amount of credit, though.
"We were playing with a team that's not quite complete, with a left-back at centre-half.
"There were all kinds of things that might not be obvious on the surface that we can take away and build on.
"We came with a shape, to make sure Ipswich didn't get behind us and did that very well.
"But although we defended well and very resolutely, we weren't able to push them back enough and ran out of energy.
"At the moment we don't have any attacking strength and that's something we hope to put right by Saturday.
"We're hoping to sign three more players by then."