The 19-year-old midfielder was given a fleeting appearance from the substitutes' bench, his first since moving from League Two outfit Exeter City in January.
And the youngster hailed Monk's policy of giving youngsters a chance to shine on the Premier League stage.
"I think the evidence is there that the gaffer will give you a chance," he told Wales Online.
"That's great to see. That's one of the things that drew me to the club - I thought if I keep training well and building myself he would give me a chance. Thankfully I have had that chance now. I think if you are good enough, you are old enough.
"It's a cliche, but if you are performing well every week there's no reason why the gaffer shouldn't put you in.
"I think a lot of the lads at this club see what Garry is trying to do in bringing young players through.
"We are all looking for a chance and thankfully I have had one now."
Grimes' next opportunity to impress could come on Saturday at home to Everton, as Swansea seek a third win in a row.
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