England led by 275 runs on first innings after winning the toss, bowling Australia out for 317 before racking up 592 in 107.4 overs, and led by 61 runs heading into the final day with Australia five wickets down in their second innings.
But after rain had limited the fourth day's play to 30 overs, it forced a total washout on Sunday, denying England the opportunity to push for victory and leaving Australia 2-1 up heading into the final Test at The Oval next week - thereby retaining the Ashes urn.
"The cricket we got in, in this game, was potentially an opportunity for a team to play it safe; to wait and see what the outcome might be," Stokes said. "We didn't do that. We definitely didn't shy away from what we needed to do.
"We're always putting our front foot forward and trying to press the game as hard as we possibly could. As a captain, that's something that makes me very proud as a leader of the ten other guys out there. It's just unfortunate that we managed to get three hours in over the last two days."
"The weather didn't help us and we can't change that. It's a tough pill to swallow, knowing that's the reason we sit here with a draw, but we've done everything we possibly could in the hours of play we managed to get. We were completely and utterly dominant throughout the hours of play we had. It's a shame, but, oh well."
When asked to compare how he felt in Manchester to his emotions after England's defeats in the first two Tests at Edgbaston and Lord's, Stokes said: "I think they're completely different.
"We obviously played some brilliant cricket in those games, [but] we played some cricket that we knew we could have been better at. But in this game I can't actually look back and think, 'We could have been better there', because we were pretty much perfect throughout the whole game.
"Bowling Australia out and then scoring the runs that we did at the pace that we did - I can't really say we got anything wrong about this game, to be honest. It is tough to say we ended up with a draw when we've dominated the cricket that we've managed to get in."
"It's very similar to 2019, when we had to go to The Oval and win to draw the series," Stokes said. "We'll have to get over the disappointment of today and then focus on that game. It is a massive game for us and 2-2 sounds a lot better than 3-1.
"The mentality and mindset within the dressing-room is to go out and win. Go back to the Pakistan series, where we could have taken it easy in that last game knowing we'd won the series but we didn't. We still went out with the same mentality of how we wanted to play our cricket.
"Every time we walk out on the field, that's all I encourage the players to do: just concentrate on what you need to do as an individual to influence a game in the right way. If it doesn't happen, you've still got an opportunity to do that in a different way or a different session. Everything we do is to try and be positive and get a result for England."
Stokes acknowledged that a decider at The Oval would have been "a very, very special week in the history of English cricket" but said that his team have "already done wonders" for the sport across the country.
"It would have elevated everything that the series has already done for Test cricket, especially in England," he said. "But I think what we've managed to do, up until today anyway, has already done wonders for cricket in England.
"I think we'll still have the support that we have done throughout the series next week. We'll be treating it as every other game and I hope the support we get will still be there or thereabouts, as if it was 2-2."
Matt Roller is an assistant editor at ESPNcricinfo. @mroller98