Bowen opened the scoring after just four minutes against the Championship side, but Bristol City stayed in the game and equalised just after the hour mark through Tommy Conway.
Paqueta went down early with a suspected knee injury at the London Stadium and had to be replaced after just 14 minutes, while Bowen made it to the end of the game but received treatment, apparently on his left ankle, in stoppage time and limped off after the final whistle.
David Moyes did not give details on the concerns, with the club waiting to see the results of scans, but is obviously hopeful they are not serious.
‘You will pick up injuries and you have to deal with it,’ said Moyes. ‘We’ve been quite fortunate this season as we’ve not picked up too many, but today we just felt as if we had one or two injuries.
‘Vladimir [Coufal] was also stunned by a couple of challenges, but we’ll check them and hopefully they’ll be OK.
‘We had a few knocks and bruises, but that’s what happens this time of year.’
Moyes did comment on the performance of Danny Ings, who came off the bench but has been linked with a move away from the club this month and Wolves touted as a possible destination.
‘I thought he played really well when he came on today. I thought he linked us up and played really well,’ Moyes said of the forward.
Asked if that meant he was a player he would like to keep hold of, the Scot said: ‘I just said he played really well in the game today.’
Hammers midfielder James Ward-Prowse admitted it was a disappointing result but looks forward to the opportunity to put it right in the replay.
‘I think we started the game really well, penned them in and showed our quality early on, but after that we seemed to drop our standards overall and they deservedly got back in the game,’ said the England international.
‘Overall it’s a disappointing result. We’d have liked to do it today but we’ve got to go again now.
‘The positive is we still have the chance to go through to the next round and still a chance to win silverware.
‘That’s the main thing and If it takes another game to do it, then so be it. Hopefully it will be worth it in the end.’
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