Thistle could count themselves unfortunate not to have taken something from their trip to Fir Park on Saturday afternoon where they lost out to a John Sutton goal, but they have the opportunity to bounce back quickly.
They host Cowdenbeath in the second round of the cup tomorrow and although Archibald has a couple of injury headaches, he will aim to field as strong a squad as possible.
"There are a couple of knocks there," he said. "We'll see how they are.
"We have had a poor run in that League Cup. We want to stay in it for as long as we can so it'll be getting addressed the same as a Premier League game, to be honest."
Saturday was Thistle's first defeat of the season but, for all that they were lethargic in the opening 45 minutes, they had plenty of the ball and plenty of chances in the second period.
Indeed, the last quarter of the game was a tense affair for the hosts as Thistle did everything but put the ball in the back of the net.
It left Archibald somewhat frustrated but, truth be told, overall it has been a decent start to life in the top flight for a Thistle side who do not look out of place by any means.
"It was a sore one to take. We didn't turn up in the first half, we know that, but we came out a bit stronger in the second half," said Archibald.
"We stood off Motherwell in the opening 45 minutes and it is probably as poorly as we have played in the SPFL this season.
"You always know that the first goal is going to be so important and Motherwell got that and then took great confidence from that.
"We are looking for the players to take a wee bit of responsibility and they did that in the second half. We need them to do that a bit earlier and to believe in their own ability.
"We probably did enough with the pressure we had to get a goal, although you could always say that they could have hit us on the counter because they broke away a couple of times and they could have picked us off."
It is a big week for Thistle, who will start their preparations for the weekend game against St Mirren once they have taken on Cowdenbeath tomorrow night.
St Mirren have found themselves under pressure after a difficult start to the season - the Saints lost at the weekend to Ross County - and any kind of result against Danny Lennon's side would not only heap more pressure on the Saints boss but also keep Thistle in a decent league placing.
And while Archibald couldn't hide his disappointment at the manner in which his side lost to Motherwell, he believes that the manner and spirit in which his side are trying to play football means that there isn't too much he feels his side should be doing differently.
"When you are going to tough grounds like Fir Park at the weekend and Paisley this weekend, the first goal is vital," he said. "But we will keep on trying to do what we are doing.
"It is important that the players believe in one another and work hard to help one another out. If you can see that someone is having a bad day then you need to go and try and help him out and take a bit of pressure off him.
"We need to work as a unit but overall we are pleased with how it is going."