Below is for those that can't earn green packs or tokens from offers and won't be buying tokens.
The provided green packs by the game (from the training facility, substitution bonus, and gifts from friends) won't be enough, especially if you have not reached to a certain game level where all facilities have been developed to maximum.
Even with 22 players, it is difficult to keep all the bonuses to 10%, especially before the first match of the day that is usually in the morning. Also, some bonuses are more difficult to maintain, for example the attacking bonus, unless you have way to much attackers than usually required for a squad of 22 players. As an indication, my team's training bonuses usually lies in the 6-10% range, where the average being around 7-8%. It is hard to keep all the bonuses at 10% before each match.
22 players may not be enough if you have to use tactics that consumes more condition for say 1 match in every 3-4 matches. 2 matches requiring full pitch pressing in the space of a day or two, and you won't be able to maintain the bonuses as you will have to let your players rest more. Once the bonuses drop below 6%, it will cost you a lot of green packs to bring them back to 10%. Also, if those two matches are close to each other, say 3-9 hours, you will definitely need to use green packs.
The red packs provided by the game only are definitely not enough. 1-2 periods of excessive injuries will likely exhaust the red packs that you accumulated, and will even force you to sell your injured players.
All that being said, you can still win a competition without buying tokens or completing offers, but it will be hard to compete in all 3 competitions with limited resources and a squad of 22 players. It will also be hard to win at least a competition every season. Last season, my team won the league (and undefeated too for the 26 matches), was Cup finalist, and was knocked-out at the 1/16 stage of the C.L. I did all that with a team around 90-100% in quality. I did not buy any scout players, any recommended players, any negociations' players and also I did not do any power-training.
There is no need for a lot of 7-8-star players, nor is there the need for a lot of special abilities or multi-positions. Special abilities are bonuses; multi-positions are for convenience; 7-8-star players are usually needed mostly when you are put to play against higher level active teams in the Cup. Don't get influenced by what you see here on some posts on this forum. Power-training, training for additional positions and for special abilities are a waste of money, that is if you have to buy tokens and turn to green packs to do those trainings. It is better to buy the close to 7 stars scout players or recommended players than choosing the more expensive option which is power-training 5-star players that were bought from the auction market. Some users might tell you that the so called fast-trainers last longer than scout players, but the way this game functions, you will have to changed most of your players every 2-3 seasons unless you use a lot of green packs to keep them up to the required standards each season. Power-training is only worthy if the user can get a lot of green packs from offers.
So, briefly, a manager with limited resources (tokens, green packs and so on) can win competitions with a decent quality team (around 100%) using good management and good tactics; the only major problem is when excessive injuries occur.