The 19-year-old midfielder scored one goal and made another against the League Two side in his first FA Cup appearance after being handed a start in the absence of several first-team players who tested positive for Covid-19.
“He is a great player who is still developing quite a lot, but there is a lot of talent there,” Borrell told ITV Sport. “Hopefully very soon he can play more games with us like [team-mate and England midfielder] Phil Foden a couple of years ago.
“They are completely different players. Phil Foden has had more opportunities and he is established. Cole has the talent and ingredients.”
City manager Pep Guardiola was missing from the dugout at a packed County Ground, as he and 20 of his players and staff were isolating after testing positive for the virus.
Despite seven first-team players being among those who could not travel, the Premier League leaders named a strong team and were merciless against a side 72 places below them in the English football pyramid.
Bernardo Silva met a low cross from Palmer to put last year’s beaten semi-finalists ahead early on, with Gabriel Jesus making it two after the Robins gifted the visitors possession on the edge of the area.
Ilkay Gundogan beat Lewis Ward with a free-kick from 25 yards to make it 3-0, but the Swindon goalkeeper did well to save a Jesus penalty minutes later after Silva was fouled by Jordan Lyden inside the box.
Harry McKirdy pulled a goal back for the hosts late on, only for Palmer to complete the scoring for City with a brilliant finish from a tight angle.
Palmer said he “enjoyed” the game and hopes Guardiola did the same, despite not being there.
“There is always that bit of pressure coming into the team being young but you have to go out there and enjoy it,” he said.
Depleted City still packed with stars
While Guardiola had to follow the game from afar, his assistant – and stand-in boss against Swindon – Borrell revealed before the game that the 50-year-old would remain “connected” with those that made the trip to Wiltshire.
Four changes were made to the City side that beat Arsenal 2-1 on Saturday, despite the club being hit by an outbreak since that game.
Raheem Sterling, Foden and Jack Grealish were among those not travelling, but defender Kyle Walker was recalled and midfielder Gundogan was handed the captain’s armband on his return to the starting XI.
Midfielder Palmer made an immediate impression with fine work on the edge of the box to create space to tee up Silva for a close-range finish for the opener.
Silva could have had a hat-trick before the break, but wasted chances either side of that goal.
Swindon gifted City their second as they tried to play it out from the back. Jesus collected possession and traded passes with Kevin de Bruyne before coolly beating Ward.
Gundogan’s free-kick just before the hour put the result beyond doubt, but Ward’s penalty save and McKirdy’s fine low finish to beat Zack Steffen at his near post ensured Swindon fans had plenty to celebrate even though Palmer emphasised City’s dominance with the pick of the goals late on.
Ward again did well to limit the scoreline in the final minute of normal time, tipping a fierce Rodri effort onto the bar.
For Swindon, hosting the Premier League champions came as a major boost for a side still rebuilding under owner Clem Morfuni.
When the Australian businessman completed his takeover just three weeks before the start of the season, Swindon had no manager and just nine senior players on their books.
McKirdy, who scored four of Swindon’s five goals in their league win against Northampton six days earlier, gave the home fans a moment to savour as Ben Garner’s side hit the six-time FA Cup winners on the counter.
But by that stage, City’s place in Saturday’s fourth-round draw – to be shown live on the BBC Sport website before Arsenal’s trip to Nottingham Forest at 17:10 GMT – was sealed.